But he blamed French and German "intransigence" and pressure from Eurosceptic Conservatives for putting the PM in "a very difficult position".
Initially Mr Clegg said the coalition was united over the use of the veto.
But he told the BBC he had "made it clear" to Mr Cameron it was "untenable" for him to welcome the move.
Sources close to Mr Clegg have told the BBC he "couldn't believe it" when he was told the summit in Brussels had "spectacularly unravelled".
The prime minister blocked changes to the EU's Lisbon Treaty at an EU summit, arguing that the proposed changes were not in the UK's interest.
It now looks likely that all 26 other members of theEuropean Union will agree to a new "accord"setting out tougher budget rules aimed at preventing a repeat of the current eurozone crisis.
As leader of the Liberal Democrats, Mr Clegg is far more pro-European than his Conservative coalition colleagues.
By Nick RobinsonBBC Political Editor
More from Nick Robinson
Q&A: Cameron and the EU
Interactive: How will euro crisis end?
He told the BBC's Andrew Marr programme: "I'm bitterly disappointed by the outcome of last week's summit, precisely because I think now there is a danger that the UK will be isolated and marginalised within the European Union.
"I don't think that's good for jobs, in the City or elsewhere, I don't think it's good for growth or for families up and down the country."
He said he would now be doing "everything I can to ensure this setback does not become a permanent divide".
The deputy PM said he had learned of the veto in a phone call from the prime minister at 0400 GMT, shortly before Mr Cameron gave a press conference announcing it publicly.
Asked what his reaction had been, the Lib Dem leader said: "I said this was bad for Britain.
"I made it clear that it was untenable for me to welcome it."
The new accord will hold eurozone members to strict budgetary rules including:
Mr Cameron has said he was seeking certain "safeguards" from Europe on protection of the single market and the UK's financial services industry.
By Robert PestonBusiness editor, BBC News
More from Robert Peston
But French President Nicolas Sarkozy called those demands "unacceptable".
Mr Clegg said unwillingness to negotiate from France and Germany, combined with "outright antagonism to all things European" from parts of the Conservative Party, had left Mr Cameron in a difficult position.
"He couldn't come back to London empty-handed because self evidently, if he'd done so, he wouldn't have been able to get whatever had been agreed through the House of Commons so all we would have had would have been a delayed crisis."
On Friday, a spokesman for Mr Clegg said he had been "consulted throughout" the 10 hours of unsuccessful negotiations in Brussels - a claim backed up by Foreign Secretary William Hague.
He told the BBC the Lib Dem leader was fully "signed up" to the decision to veto the proposed treaty.
Mr Cameron will make a statement in the House of Commons on his decision on Monday - and the Labour leader called on him to use it to "explain why he did something that was so bad for Britain and bad for British jobs".
"He did this because the Eurosceptic wing of the Conservative Party has effectively taken over and that isn't good for the national interest," Ed Miliband said.
"What I say to Liberal Democrats and others is that we will work with anybody who thinks this position cannot stand. We must find a better way forward for Britain."
Mr Hague insisted Britain was "not marginalised", and told Sky News that while "everybody knows" that the Tories and Lib Dems had different views on Europe, the negotiating position taken by Mr Cameron "was agreed in advance" with Mr Clegg's party.
But Lib Dem peer Lord Oakeshott said his party's Business Secretary Vince Cable had "given a very serious warning last Monday in the cabinet against elevating these financial regulation points into a make or break deal".
Asked about Labour's allegation that Mr Cameron did not genuinely want to reach a deal in Brussels, Lord Oakeshott told the BBC's Politics Show he believed "a walk-out quite suited him".
Mr Cameron and his Chancellor George Osborne have insisted the veto was in part to protect the City of London from excessive intervention by Europe, but Labour and the UK Independence Party have both warned that actually no additional safeguards for it were achieved.
UKIP leader Nigel Farage said the City was "under very serious threat" of "retribution", adding: "Every time the bond markets twitch I can see the finger being pointed at those awful Anglo Saxons in the City of London."
The BBC's business correspondent Joe Lynam said it was not yet clear whether the City would be better or worse off in the long term.
But he said there was a risk that British banks could be affected by deals done by the remaining 26 EU member states which cannot be blocked as unanimity is no longer required except in the case of taxation.
Deputy Prime Minister Nick Clegg says David Cameron's veto of EU treaty changes was "bad for Britain" and could leave it "isolated and marginalised".