Conservative peer Lord Lawson laughed off the attempts from the Labour peer, suggesting no-one else in the upper chamber "takes it seriously".
As speaking at the House of Lords began for two days of debate on the Government's Article 50 Bill, Lord Mandelson told peers: "As is well known, I was a Remainer. Not – I might say – because of my pension rights but because I am a patriot. A patriot rather than a nationalist.
"And that's why I think the approach the Government has decided to take to Brexit is wrong."
The ex-business secretary repeated former Labour prime minister Tony Blair's claim that Theresa May is chasing "Brexit at any cost".
Lord Lawson took aim at Lord Mandelson's anti-Brexit stance
I think he is really still in the Tony Blair camp of trying to get the whole thing reversed
Criticising Lord Mandelson's intervention, Lord Lawson told BBC Daily Politics: "I think he is really still in the Tony Blair camp of trying to get the whole thing reversed. But, nobody takes it seriously."
The Labour peer is among pro-EU peers bidding to guarantee the rights of EU citizens living in the UK.
"I have come out clearly all along that we should give a unilateral guarantee to those European Union citizens who are legally resident here at the time of the referendum," said Lord Lawson.
However, he declared the House of Lords "not to be the place" to discuss this issue, adding: "Home Secretary Amber Rudd has already given an undertaking to the Commons that they'll be no question of having them removed without a vote in the House of Commons."
Lord Lawsons also declared British nationals living in other EU member states have no reason to be "anxious".
The 84-year-old also sought to reassure Brexiteers that only a small are hoping to delay or stop Brexit as Mrs May's Brexit Bill is debated in parliament's upper chamber.
"There won't be any ping-pong, even Angela Smith – the leader of Labour in the House of Lords – has made it absolutely clear, even if she would like to see one or two amendments made, when they go to the House of Commons, and the House of Commons says, 'No thank you,' that will be the end of it," he concluded.
Lord Mandelson has been slated for his participation in the minority group of peers seeking to force changes to the Brexit Bill while still earning tens of thousands of pounds from Brussels.
Remoaner-in-chief: Blair's Views on Brexit Fri, February 17, 2017
Blair will just not give up.
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'It can be stopped, if the British people decide that having seen what it means, the pain-gain analysis doesn’t stack up'
The peer, alongside Lord Kinnock, Labour's former leader, and Lord Patten, who served in Margaret Thatcher's cabinet, all receive EU pensions.
Many other former MEPs and European commissionaires are also receiving payouts from a Brussels pension pot estimated to be worth £10 million.
Dominic Raab, a former justice minister, said: "Lords with generous EU pension pots should be open with the British people and declare this when they speak in parliament on Brexit.
"It's time the Lords came clear about their EU money and recognise the decision of the people by backing the Article 50 Bill unamended."