Mr Cameron said he was heartened that, for the first by-election in a long time, the Tory candidate also picked up votes from the Liberal Democrats.
Speaking outside his London home, he said: "To have a further swing to Conservatives in such a strong Conservative seat, I really think is a very good result.
"It is obviously a disastrous result for the Labour Party, but I think I am right in saying it is the first time in a long time when there has been a contest between Conservatives and Liberal Democrats when there has been a swing to the Conservatives.
"I think what we are seeing is that people who voted for all sorts of different parties - including the Liberal Democrats - are now looking at the Conservatives and saying "Yes, this is an alternative to the Government that I can believe in."
As expected, Conservative candidate John Howell took the Oxfordshire seat by a comfortable margin of 10,116 in yesterday's by-election, triggered by the departure of Boris Johnson to become London Mayor.
While Labour had no hope whatsoever in winning in what is natural Conservative territory, party strategists will be alarmed at the dramatic collapse in its vote in a seat where it finished third in the last general election.
Health minister Ben Bradshaw admitted it had been a "terrible result" for Labour on the first anniversary of Gordon Brown's arrival as Prime Minister.
But he blamed the economy rather than Mr Brown's unpopularity, and insisted the party had bounced back to win the general election after similarly bad performances in the past.
"That's what happens in by-elections," he told BBC Radio 4's Today programme.
"But I'm not trying to minimise my disappointment - it's a terrible result."
Mr Bradshaw said Mr Brown was working in a "very difficult context".
"We've got the credit crunch, we have got a doubling in oil prices, we have had food prices rise by 40% since the early spring. That's a difficult economic backdrop."
Mr Bradshaw added: "I don't believe he is personally unpopular, because if you drill down into the opinion polls and the focus groups' work there is almost a complete correlation between (voters') economic situation and their feelings about the Prime Minister."
Mr Cameron made clear he blames Mr Brown for much of the economic distress being suffered by voters.
"One can argue forever about all the disasters and all the incompetencies of the last year but, at a time when British families are facing higher prices at the fuel pumps and every time they do the family shop, I think the most important thing about this Prime Minister is that he was in charge of the economy for 10 years and he didn't put aside money in the good years.
"As a result, at the time when people need help, the cupboard is bare. I think that is the most damning thing of all."
Despite a second by-election victory coming hot on the heels of the remarkable capture of Crewe and Nantwich from Labour last month, Mr Cameron insisted there would be "no complacency, no triumphalism" from his party.
"We have got a lot of work still to do, but I think this is another good step forward for the Conservative Party," he said.
Liberal Democrat leader Nick Clegg said that the result showed that Mr Brown's days in No 10 were numbered.
"After one year in the job, Gordon Brown cannot even get enough support to save his deposit," he said.
"Labour's days are well and truly over and it is the Liberal Democrats who are challenging the Conservatives in the south and Labour in the north."
Mr Howell took the seat with 19,796 votes to the Lib Dem candidate Stephen Kearney's 9,680.
Labour's Richard McKenzie could only poll 1,066 votes, behind the Green Party's Mark Stevenson on 1,321 and the BNP's Timothy Rait on 1,243.
Both the Tories and the Liberal Democrats saw their share of the vote rise slightly compared with the general election while Labour's fell by more than 11 per cent.
Tam Dalyell, the ex-Father of the Commons and former Labour MP, said: "Cumulatively it is perceived that there are some young, rather arrogant, inexperienced, bumptious ministers in the Cabinet, and people don't care for them very much.
"Let me say who I mean: Ed Balls, James Purnell, Andy Burnham, Yvette Cooper. People think it is a very unimpressive, on-the-make Cabinet. There is a common thread of a 'cheeky chappie' running through it."
* Bookmakers William Hill cut the odds on Mr Brown being replaced as Labour leader before the general election from 5/4 to 11/10 in the wake of the Henley result, and slashed odds on him standing down in 2008 from 5/1 to 3/1.
Labour are now 5/2 with Hill's to win the next election - their longest odds since coming to power in 1997 - while Tories are clear favourites at 2/7, their shortest odds since losing power. Lib Dems are 100/1 outsiders.
"Although Mr Brown is a slight odds-on chance at 4/6 still to be leader when the general election comes round, we haven't taken a single bet of £100 or more for him to do so for months," said Hill's spokesman Graham Sharpe.
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