But he agreed with Mr Farage that a second referendum "would achieve an even stronger vote to leave".
According to Farage, pro-Europeans such as former UK Prime Minister Tony Blair "will never ever ever give up".
However, Mr Farage claimed another vote would end the "whingeing and whining and moaning" of Remainers.
Following Nigel Farage's comments on television this morning that 'Maybe there should be a second referendum' it is now 5/1 that we will go to the polls again before 2019.
Talk of a second referendum - long favoured by Remain backers - has come to the fore in recent days after Nigel Farage, one of the architects of Brexit, said he believed there is now an argument to say one should be held. Adonis added: "Farage wants a referendum on Mrs May's Brexit deal". The former UKIP leader predicted that another vote would see voters back the move in "very much bigger" numbers.
Nigel Farage isn't a UK MP, but he is a member of the European Parliament, and also commands huge amounts of air time and newspaper column inches in the UK, and increasingly in the United States, as a prominent supporter of Donald Trump and a Fox News contributor.
Andrew Adonis, who recently called on Jeremy Corbyn to back a second referendum, took to Twitter to say "bring it on", with the same words being used by chair of anti-Brexit organisation Best for Britain, Lord Mark Malloch.
"If we do not act radically now, we will sleepwalk into a faux Brexit, in name only", he said in a statement today.
Former Lib Dem leader Mr Clegg tweeted: 'I agree with Nigel'.
'With these comments Nigel Farage is disowning the chaos that trying to leave the European Union has wrought on this country.
Earlier yesterday in a TV interview Mr Farage revealed he was on the verge of a change of heart on a second referendum. If it's a straight "Remain" or "Leave", there's a risk a vote on principle will reinforce Brexit. Since then, the United Kingdom government has been negotiating its exit from the EU.
But Theresa May's spokesman shot down the demands, telling reporters: "As I have said before, we will not be having a second referendum". Previously he has insisted that the result of the 2016 referendum had to be respected.