Media captionNick Clegg: "We always knew it was going to be difficult"
Senior Lib Dems have said the party is "united" despite Thursday's rebellion over raising tuition fees in England.
Leader Nick Clegg said the party would move forward without "rancour" while Vince Cable said the coalition would be "stronger for the experience".
The government's majority was slashed as 21 Lib Dem MPs voted against the plans and five abstained.
Lib Dem minister Norman Baker said it was "embarrassing" that the party had made a pledge it could not deliver.
The vote took place against a backdrop of violence in central London, which Prime Minister David Cameron has condemned as "completely unacceptable".
He said he was "very concerned" about an attack on a car carrying the Prince of Wales and the Duchess of Cornwall, which is now the subject of an investigation by Scotland Yard.
Thursday's rebellion was the largest since the Liberal Democrats were formed, as the party split three ways on the vote.
Its MPs had come under huge pressure from protesters after signing a pre-election pledge to oppose tuition fee rises. The policy will see the basic fee cap rise from £3,290 to £6,000 and universities in England able to charge £9,000 in "exceptional" circumstances.
Ex-Lib Dem leaders Charles Kennedy and Sir Menzies Campbell were among those to vote against the government and two junior ministerial aides - Jenny Willott and Mike Crockart - resigned over the issue.
But Business Secretary Mr Cable - one of 28 Lib Dem MPs to vote for the plans - said his colleagues acknowledged that he had "considerably improved" the proposals in terms of the support for poorer students.
"It was a difficult day," he told BBC Radio 4's Today, "but I think we are stronger having been through this experience."
"We are united, we will go forward and I think the coalition will be stronger not weaker for the experience."
He said he had spoken to each Lib Dem MP before the crucial vote but denied any "horse trading" to win them over.
He added: "I think my colleagues accepted, however they voted, that I and my colleagues in the government, we acted responsibly, that we had protected universities and maintained them as viable and strong institutions and produced a policy towards future graduates which is fairer and more progressive than the system we inherited."
Asked about Nick Clegg's future, Mr Cable said he was "absolutely confident" that he would continue as leader and the Lib Dems would continue as a party within the coalition.
On Friday, Mr Clegg said the rebellion was "no surprise", given the different views in the party.
He said: "We, internally within the Liberal Democrats, knew that we wouldn't be able to find complete unanimity in this, clearly we did not.
"It's no surprise to anyone that this was going to be a difficult issue for us. But, we've talked to each other and the party has discussed this in a calm and respectful manner, which I think will now allow us to move forward without rancour and in a united way - not least in the coalition government - so that we can deliver the liberal, fair-thinking things we want for Britain as a whole."
But Lib Dem Transport Minister Norman Baker, who voted for the policy, told BBC Radio 5live the party had got itself in "the wrong place".
"We made a pledge we could not deliver which I believe is deeply regrettable and rather embarrassing," he said.
He said the proposals were better than those recommended by the independent Browne review but were "not perfect". If Lib Dems had opposed the policy it would have meant "the end of the coalition", he said.
"None of us like the policy which has emerged particularly," he added. "In a way, I'd rather have had a different solution but we did face a couple of pretty unpalatable alternatives."
Another of those to vote for the proposals - Don Foster - said his constituency office in Bath had been attacked afterwards. One window was smashed when it was hit by a small rock but no "serious damage" was done.
Six Conservative MPs voted against the tuition fee rises while two abstained in Thursday's vote.
One of those who abstained, Lee Scott, said the party was well aware of his views and he had disagreed with tuition fees since they were introduced by Labour. "I just could not vote for it," he told BBC 5live. "I did what I believed was right."
Student leaders and Labour, who favour an alternative graduate tax, believe higher fees and the fear of student debt will put people off going to university.
Shadow Home Secretary Ed Balls said the tuition fees battle showed the Lib Dems had become "human shields" for their coalition partners.
"Week after week it is Lib Dem ministers like Danny Alexander and Vince Cable who find themselves in TV studios defending what are essentially Conservative policies in a predominantly Conservative government," he wrote in an article for Tribune magazine.