Admitting it had "always been a difficult issue" for the Tories, he insisted the "important thing is to do the right thing for the country".
Speaking during a visit to Lockheed Martin UK in Bedford, Mr Cameron defended his decision to impose a three-line whip on his MPs over the vote, saying "in politics you have to confront the big issues rather than try and sweep them under the carpet".
"It wouldn't be right for the country now to have a great big vote on an in/out referendum and the rest of it," he added.
"What I would say from last night is there's no bad blood, there's no rancour, no bitterness."
Conservative MPs inflicted the biggest ever Tory rebellion over Europe on the Prime Minister last night when 79 backbenchers defied orders by voting for a national poll on British membership of the European Union.
Mr Cameron attempted to play down accusations that the party had been left deeply divided by the scale of the rebellion - the biggest assault on his authority since he became Conservative leader six years ago.
He added: "These are valued Conservative colleagues. I understand why people feel strongly and we will go forward together and tackle the difficult decisions that the country faces.
"But you have to do the right thing and give a lead in politics and that was what yesterday was about.
"First of all the country has a guarantee now in law that if ever there is a proposal to pass power from Westminster to Brussels we would ask people in a referendum first.
"That is written into the law of the land and that's right but the real focus for Europe right now has got to be to solve the eurozone crisis that is having a chilling effect on our economy."
Mr Cameron insisted the priority for Britain was creating growth, which meant "making the market work" and "opening the single market".
"Those are the things Europe needs to focus on, not the interference in people's everyday lives.
"We have got to make sure the single market is working for Britain, get regulation off our businesses, keep taxes low, make sure in Europe we are fighting for open markets and trade, not interfering in the everyday lives of people.
"That's what I'll be fighting for and we can now do that united."
Among the rebels were two ministerial aides, Adam Holloway and Stewart Jackson, who voted for a referendum knowing they would lose their unpaid Government jobs.
A Downing Street spokeswoman confirmed that both men had been "removed" but not "sacked" from their positions.
"They haven't been sacked because they were told in advance that if they voted that way they would be removed from Government."
She added: "The difference is they knew that was the consequence of their actions."
Deputy Prime Minister Nick Clegg condemned the backbench rebellion as a "smash-and-grab dawn raid".
During a visit to London's East End, Mr Clegg said Britain should be leading, not leaving Europe.
Recognising that reforms to the EU were necessary, he said: "You don't change Europe by launching some smash-and-grab dawn raid on Brussels.
"You do it by setting out the case for changes and then arguing the case with other countries.
"We can't do this on our own - we have to build alliances, we have to convince and persuade other countries and that is what we look to do all the time."
Education Secretary Michael Gove told the BBC he would like to see "a change in this Parliament" on Britain's relationship with Europe.
He added: "We are already winning powers back - we need to win more and that process will require careful negotiation but what we are fortunate in having is a Conservative Party that is united as never before behind that renegotiation."
Mr Cameron's official spokesman rejected suggestions that the comments by Mr Gove and Mr Clegg indicated a rift within the Government.
The coalition agreement published last year made clear that the Government would "examine the balance of the EU's existing competencies" and in particular seek to limit the application of the working time directive in the UK, he pointed out.
"We have a coalition Government and some of the things that Conservative members of the Government are saying reflect Conservative Party policy and some things reflect the Government's policy," said the spokesman.
"The Government's policy is very clear, because it is set down in the coalition agreement."
When Mr Cameron told MPs in the Commons yesterday that he was "firmly committed... to bringing back more powers from Brussels", he was speaking in his position as Conservative leader, the spokesman indicated.
The spokesman confirmed that Mr Cameron and Mr Clegg have discussed Europe several times recently in their regular meetings, but that their focus has been on the current crisis in the eurozone.
The work of examining the balance of the EU's competencies was ongoing within Government, with the Foreign Office in the lead, he said.
But he was unable to say when an opportunity may arise to negotiate changes to Britain's relations with the EU, suggesting that a large-scale amendment to treaties "may be some years down the line".
It was necessary to draw a distinction between a major treaty change of the kind seen in Nice in 2001 and Lisbon in 2007 and a minor amendment which simply changes a few words.
"They are different things and if you are in negotiation you approach those things differently," said the spokesman.
He added: "There is a series of negotiations that will be coming up at European level. One of those potentially may involve some limited changes to treaties. That is what the European Council decided on Sunday.
"As the thinking on that develops, we will be developing our thinking about how best we can further our interests in those negotiations.
"As the Foreign Secretary and Prime Minister were saying yesterday, the priorities for us are protecting the integrity of the single market and protecting financial services."
Mr Clegg ruled out any prospect of eurosceptics pushing Britain "towards the exit sign" while he is the Deputy Prime Minister.
"This Government, of which I'm the Deputy Prime Minister, is not going to launch some sort of dawn raid, some smash and grab raid on Brussels," he told ITV News.
"It won't work, it will be condemned to failure.
"Eurosceptics need to be quite careful for what they wish for, because if they succeed - and they won't succeed, as long as I'm in government - to push this country towards the exit sign, let's be clear: the people that will be damaged is British families, British businesses, British jobs, British communities, and I won't let that happen."
Conservative MP Andrea Leadsom, who joined the rebels last night, said her ideal solution would be for the Government to renegotiate Britain's relationship with Europe prior to a ratifying referendum on the results of that negotiation.
The MP for South Northamptonshire is part of a group of backbench Tories drawing up a draft White Paper for publication next year, which they say will set out the position the Government should take up in a renegotiation.
Ms Leadsom said today that Conservative ministers had offered the group encouragement.
"Certainly, Government ministers have been very warm towards the idea of us doing that work," she told BBC Radio 4's World At One.
"I genuinely believe that our frontbench on the Conservative side are Eurosceptic - they would genuinely like to repatriate powers.
"They are in a difficult position with the eurozone in complete crisis. They have to be very careful that they don't make things worse.
"But at the same time, I genuinely believe that they would welcome us doing the work to look at what a renegotiation would look like."
Ms Leadsom denied rumours circulating on the internet that she swore at Chancellor George Osborne when he called last night to try to persuade her not to rebel.
"We had a very polite conversation," she said. "We agreed to differ. I wouldn't speak to any colleague in the way I was reported as speaking to him."
Tory peer Lord Garel-Jones, who was Europe minister at the time of the rebellion against the Maastricht Treaty under John Major, suggested that a handful of MPs who want British withdrawal should quit the Conservatives and join Ukip.
Lord Garel-Jones said most of those rebelling last night were "Euro-realists" who wanted simply to defend UK interests within the EU, while the "nihilists" who actually want withdrawal could be counted "on the fingers of one hand".
He told World At One: "Those who are anti-European in the sense that they want to withdraw should consider their position.
"If you want to withdraw from the EU, there is, I believe, a little party somewhere that advocates that, but it is not the Conservative Party."
Former Liberal Democrat leader Sir Menzies Campbell said he had "no argument in principle" against a referendum, but did not believe one was likely to be held during this Parliament.
Coalition policy was to call a referendum only if there was a treaty proposing "substantial transfer of powers", he said, adding: "If no such circumstances arise, then there won't be a referendum."
Shadow foreign secretary Douglas Alexander wrote to Mr Hague warning that "disunity... between and within the coalition parties is already undermining Britain's credibility in ongoing European discussions".
He demanded to know whether Mr Cameron was speaking for the Government or the Conservative Party when he raised the prospect of a renegotiation of the UK's EU membership.
Mr Alexander later said: "Last night demonstrated that we have got a deeply-divided Conservative Party. But the comments that have emerged this morning from the Deputy Prime Minister Nick Clegg seem to confirm that we have a deeply-divided Government.
"Within a couple of hours of Michael Gove taking to the airwaves this morning promising the repatriation of powers, we have now got the Deputy Prime Minister, his Cabinet colleague, flatly contradicting him and saying there will be no repatriation of powers as part of the coalition Government's programme.
"The public deserves better than a Government turning inwards and fighting with each other instead of fighting for British jobs, British investment and British growth.
"This spectacle of an out-of-touch and divided Government is undermining the influence Britain has at the European negotiating table, which is bad news for millions of British people who desperately want to see a proper plan for growth and jobs."
PA
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