Appearing on BBC Breakfast, Mr Clegg, one of the most pro-EU politicians in Westminster, was asked by Dan Walker: “There might be many people watching and thinking ‘just accept it’.
“We understand you and many others didn’t want to leave the EU but the UK has voted to do that and that is what is going to happen so stop arguing about it.”
In response the MP for Sheffield Hallam, speaking from Brussels, said he did accept the result of the referendum but said the complication arose from how Britain would leave the EU.
Nick Clegg was asked why he does not just accept Brexit and move on
“That is not a straight forward matter and there are lots of different choices,” he said.
“As you will remember the Brexit campaign… Nigel Farage, Michael Gove, Boris Johnson. They made lots of commitments like pots of money for the NHS every week and a cut in VAT. Things they have now fallen silent on.
“But they were not articulate about what the deal actually means.”
Mr Clegg and the rest of the Liberal Democrats have repeatedly called for Britain to remain inside the European single market.
However the Prime Minister made it clear last week she will remove Britain from the single market.
Angry BBC Breakfast viewers rounded on Mr Clegg. One said: “Please tell Nick Clegg, until we leave the EU no money for NHS etc will be available as we are still paying in. That’s the reality!”
Nick Clegg has called for a second referendum to vote on the final Brexit deal
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There might be many people watching and thinking 'just accept it'
Another asked: “Does anyone listen to Nick Clegg anymore?”
A third said: “Nick Clegg should have tried harder before the vote, accept the result and move forward.”
Ian Coley criticised the BBC for booking Mr Clegg as a guest.
He posted: “Can someone have a word with Nick Clegg? He still ignores the EU referendum result! @BBCBreakfast shouldn’t give him the oxygen to talk c***.”
Other viewers offered their support to the 50-year-old with one tweeting: “There is no mandate to leave EU. Only 37% of electorate voted leave. Block Article 50 for sake of UK.”
Eleven justices – a record number to hear an appeal – listened to four days of detailed legal argument in December and will announce their much-awaited ruling on the Government's Brexit challenge on Tuesday.
The Supreme Court is set to announce its verdict on Tuesday morning
The justices stressed at the start of the proceedings last year that their task was simply to rule on an issue of law – whether the prime minister has the right to begin the Brexit process without approval from Parliament.
Supreme Court president Lord Neuberger announced: "This appeal is concerned with legal issues and, as judges, our duty is to consider those issues impartially, and to decide the case according to the law. That is what we shall do."
His remarks came after the High Court judges who originally rejected the Government's case – stressing they were deciding a "pure question of law" – faced fierce criticism from Leave campaigners and an accusation that they were "enemies of the people".
Lord Chief Justice Lord Thomas, and two other leading judges at the High Court, ruled on November 3 that Prime Minister Theresa May lacked power to use the royal prerogative to trigger Article 50 of the Lisbon Treaty and start the two-year process of negotiating Brexit without the prior authority of Parliament.
The subsequent Supreme Court hearing attracted media attention from around the globe. It was the most televised UK case ever.
The Government's top law officer, Attorney General Jeremy Wright, arguing that the High Court got it "wrong", told the justices that the use of the prerogative in the circumstances would be lawful.