The Conservative MP for Rushcliffe was appearing on the BBC’s Newsnight programme when he made the comments amid Theresa May’s “crunch” talks with the EU this week.
Mr Clarke, who is a staunch Remainer, argued if the Brexit talks were left to “the politicians, diplomats and officials within governments”, the EU 27 would agree on a deal “probably in a month or two”.
The Tory claimed the problem lay with the UK Parliament because it was so deeply divided on the European issue.
He said: “I have never known a more pathetic Parliament.
“The Parliament has so far failed to exercise any real influence over events.
“That is why you have referendums to neutralise parliaments and parties.
“Both parties are shattered and hopelessly divided – they can’t agree even among themselves.
“And you can’t get an agreement in Brussels which can get a majority in the Cabinet or can shut up the Brexiteers.
“Parliament has got to start functioning properly.”
He added: “In the end, we are a parliamentary democracy.
“I don’t think we should have decided all of this with one daft opinion poll.
“I want to see parliamentary democracy function properly.”
Mr Clarke maintained the UK would not make the “terrible” error of reinstating a hard border in Ireland to avoid breaking the Good Friday Agreement.
The Father of the House of Commons argued the Government would not row back on its achievement of ending “years of violence and struggles” in the region.
He said: “For as long as it takes we are not going to make the terrible error of restoring a hard border in Ireland.
“The symbolic effect would be catastrophic.”
The ardent Remainer, who believes “we have thrived in the European Union”, also said it would take much longer than two years to settle all the arrangements we need to with the EU.