But the Prime Minister rejected calls from Richard Taylor, the father of murdered schoolboy Damilola Taylor, for Mr Clarke to be sacked, saying he had a "hugely difficult job to do in trying to deliver more for less".
Mr Cameron also insisted that being prepared to "listen to what people say and come up with something better" was "a strength in politics, not a weakness, and certainly something Ken has no problems doing".
Scrapping plans to increase the reduction given to criminals who plead guilty early, which would have saved £130 million, Mr Cameron said it would have sent "the wrong message".
"Public confidence isn't a side-issue in this debate, it is the issue," he said.
"The sentence served would depart far too much from the sentence handed down by the judge, and this is simply not acceptable.
"The sentence would be too lenient, the wrong message would be sent out to the criminal and it would erode public confidence in the system."
The savings will now be sought through "efficiencies" elsewhere in Mr Clarke's department, Mr Cameron said.
He indicated that the Probation Service had suffered less in cuts so far than the police and was not safe from the fallout from the latest changes.
Asked if a deal had been struck to protect it, he said: "We have not made that agreement. The proposed efficiencies in the Probation Service are less at the moment than the efficiencies we are making, for instance, to the police service."
Speaking at a Downing Street press conference, Mr Cameron said the current system was "failing and badly needs reform".
He also announced plans to review the use of indeterminate jail sentences for the public protection, saying they could be replaced.
Plans for the alternative include a "greater number of life sentences, including mandatory life sentences for the most serious repeat offenders", the Premier said.
"Instead of serious, sexual and violent offenders being released halfway through their sentence, we propose they should spend at least two-thirds of that sentence in prison, and that such offenders should never again be released early without the parole board being satisfied that it is safe to let this happen."
Dangerous offenders should also take part in compulsory programmes behind bars to make them change their behaviour, he added.
"The public need to know that dangerous criminals will be locked up for a very long time. I'm determined that they will be."
The sentencing U-turn comes a week after former health secretary Alan Milburn branded the coalition's watered-down NHS reforms the "biggest car crash" in the service's history.
The justice bill includes a compulsory jail term for anyone threatening someone with a knife, he said.
A criminal offence of squatting is planned, along with stronger measures to protect homeowners defending their property.
"We will put beyond doubt that homeowners and small shopkeepers who use reasonable force to defend themselves or their properties will not be prosecuted."
In a written statement to MPs, Mr Clarke said community sentences would be made "tougher", with longer curfews, a ban on overseas travel, and "properly-enforced financial penalties, including seizing assets from those who do not pay".
Community service will be overhauled "so that offenders work longer hours, carrying out purposeful, unpaid activity that benefits their local community".
And powers to take money from prisoners' earnings to support victims will be extended, he said.
Five drug recovery wings in prisons will be piloted as part of moves to get more offenders off drugs and alcohol, and payment-by-results schemes designed to cut reoffending will be extended, with services delivered by the voluntary, independent and public sectors.
A "clear national framework for the use of out-of-court disposals, reforming the use of remand, and reducing the number of foreign national offenders" will also be brought in, Mr Clarke said.
Many of the Government's measures risk increasing the prison population in England and Wales, which stood at 85,345 on Friday, just 150 short of last October's record high of 85,495.
Each prison place costs about £45,000 a year, with almost one in two offenders reoffending within one year, Mr Cameron said.
Gemma Lousley, of the Criminal Justice Alliance, which represents more than 50 criminal justice organisations, said: "Continuing to pour money into a bloated prison system whilst cutting funding to probation and community programmes, which are cheaper and more effective than custody, is a hopeless waste of resources, while introducing a new mandatory minimum sentence is neither a necessary nor an effective response to the problems of knife crime.
"If the Government is truly committed to a 'rehabilitation revolution', it needs to set aside unhelpful tough-talking on crime, and focus on efficient and effective responses to offending."
Shadow justice secretary Sadiq Khan added that the Government's policies on law and order were "in complete shambles".
"They do not have a coherent strategy for cutting crime because they are obsessed only with cutting costs," he said.
"Asking those services that deliver rehabilitation and protection of the public to bear the brunt of the cuts to the justice system at the same time as keeping more offenders in the community is simply irresponsible."
But the crime reduction charity Nacro welcomed the reforms as a "once-in-a-generation opportunity" to focus on reducing reoffending, reducing crime and protecting victims.
And former Tory home secretary Lord Howard told BBC Radio 4's The World At One that the Government had taken a "perfectly sensible" approach.
Mr Clarke later told MPs he considered introducing a "greater degree of judicial discretion" in an attempt to keep his plans to halve sentences for those who plead guilty early, but added that the Government "could not make that work".
Outlining the justice bill, he said he would reintroduce a mandatory life sentence for "the most serious repeat offenders".
He also confirmed the Government's intention to introduce a full 40-hour working week across prisons.
Plans to bring in the six-month mandatory minimum sentence for any offender who threatens a victim with a knife are expected to cost £5 million and increase the number of prison places used by 100, an impact assessment released by the Ministry of Justice showed.
But overall, the justice bill is expected to save 2,650 prison places and £80 million.
Reducing the use of remand is expected to save up to 1,400 prison places and £40 million.
Deporting foreign nationals serving indeterminate sentences at the end of their tariff period is expected to save another 300 places and £10 million, with another 250 places and £10 million also being saved by giving foreign nationals conditional cautions if they leave the UK.
Mr Clarke also plans to remove "some of the statutory restrictions in the use of fixed-term recall and executive re-release" to reduce unnecessary use of Parole Board resources.
The move is expected to save up to 300 prison places and £10 million.
And diverting offenders with mental health problems from custody to treatment will save up to 750 places and £20 million, the assessment showed.
The proposals outlined last September were expected to save £210 million, some £130 million more than the measures in the bill.
Mr Clarke also outlined plans to deduct 40% of earnings from prisoners working on licence in the community, generating around £1 million a year which will go towards victim support services.
Under other measures outlined today:
:: Offenders who fail to comply with community sentences will face fines of £2,500;
:: Offenders in the community will face 16-hour curfews for up to 12 months, an increase from the current 12 hours;
:: Offenders will also have their cars clamped and sold if they do not pay back their legal aid debts.
The drug free wings of prisons will be piloted in Bristol, Holme House, Brixton, High Down and Manchester.
"The priority behind our reforms is public protection and cutting crime," Mr Clarke said.
"We want to attack the shamefully high rate of reoffending and that means cracking down hard on drug abuse inside prison.
"That's why we are today launching ambitious new drug recovery wings which will get prisoners clean and stop them committing more crime.
"As well as hard work inside prisons, we will introduce for the first time a focus on the most effective means of reducing reoffending, and have made clear that we will pay providers for services that successfully protect the public from repeat criminals."
Plans to seize items such as cars or TVs from offenders who persistently refuse to pay fines will be piloted in Cheshire and Norfolk from this summer, the Ministry of Justice said.
Frances Crook, director of the Howard League for Penal Reform, said the new proposals on knife possession were "worrying".
"It is disappointing to see mandatory sentences being introduced that compromise judicial discretion," she said.
"It is also unclear what the need for a mandatory sentence is, as there is already a downward trend in convictions.
"Nonetheless, given around 5,000 people are convicted of carrying knives each quarter, what constitutes using a knife to threaten will have to be very tightly defined to avoid prison numbers spiralling out of control."
Victims' Commissioner Louise Casey backed the plans to toughen up community sentences and to abandon the proposals to halve sentences for guilty pleas.
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