The vote on September 18 is "the Labour Party's fault", Glasgow MP Ian Davidson said.
Despite his avowed unionism, Mr Davidson said the referendum debate, in which he has been heavily involved as convener of the Commons Scottish Affairs Committee, has been "immensely constructive and positive".
Politicians should take these lessons forward for a referendum on the UK's membership of the European Union, "an elite project which has gone way beyond the original intentions of its founders", he said.
North East Scotland MSP Jenny Marra agreed that Labour has been "complacent" and has yet to learn the lessons from the SNP about rejuvenating the party.
She marched outside her own party conference in 2003 in protest against Tony Blair's march to war in Iraq, she said.
But she challenged the view that the Scottish referendum debate has been constructive and rejected calls for an EU referendum.
Mr Davidson said: "The experience of the Scottish referendum is making me ever more convinced that we need to have a referendum on the EU.
"I think the way that the referendum came about and has developed has actually been immensely constructive and positive for those of us involved in politics.
"Quite clearly why we have got into a referendum in Scotland is because people were enormously unhappy with what was on offer at the time, and I think that was our fault. That is the Labour Party's fault.
"The traditional view that the working class had nowhere else to go was shown to be wrong as soon as they did have somewhere else, just as in the rest of the UK Ukip are demonstrating that if working people have somewhere else to go then they will go there if they are not satisfied.
"When Labour in Scotland attached themselves to New Labour, with its policies of privatisation and kowtowing to the Americans, we quite clearly got ourselves out of step with the majority of Scottish opinion."
He added: "The EU is an elite project which has gone way beyond the original intentions of its founders.
"The fact that we voted to stay in a free trade area all those years ago has been taken as the green light for ever closer union, for the sucking of powers to the centre just as Edinburgh and Holyrood are sucking powers from the rest of Scotland.
"People have never actually been asked, and I therefore think that the opportunity that we are being given to look over the cliff to separation is actually quite a constructive thing."
Ms Marra, a former Labour spokeswoman in Brussels, said: "I think a referendum on the EU is completely the wrong thing to do at the moment.
"I completely agree with Ed Miliband's position on this, as I think most people in Labour do.
"Those of us sitting in Holyrood every day can already see the amount of government business that is so directed towards the referendum.
"Every debate is pinned on this thing, and if the whole of the UK were to engage in a referendum on the EU it would be a massive distraction at a time when the economy is starting to recover."