Lord Mandelson accused Ed Miliband of throwing away a genuine chance of returning the party to power by shifting the party to the left.
He said the party leader had delivered “a passionate and a professional performance” in the campaign but had seriously misjudged the public mood.
“The awful, shocking thing about this election is that Labour could have won it or at least come a very near second. The reason we lost it, and lost it so badly, was because in 2010 we discarded New Labour rather than revitalising it and re-energising it and making it relevant for new times that we faced.”
His views were echoed by former Prime Minister Tony Blair who said in an article for The Observer that Labour had to regain the centre ground to stand any chance of being elected.
The party now faces an agonising process in selecting a leader who can feasibly challenge the Tories in 2020.
Barnsley MP Dan Jarvis has been widely tipped on social media with Bassetlaw MP Jon Mann saying the former solider would be the ideal candidate.
Front-running candidate Chuka Umunna remains the bookmaker’s favourite. Speaking on Andrew Marr Show the Shadow Business Secretary said he would “play the fullest part I can” in rebuilding the Labour Party but declined to confirm that he would seek the leadership.
Blairite Liz Kendal indicated in an article for the Sunday Times she was mulling a bid while Shadow education secretary Tristram Hunt said he is “definitely thinking about” running.
He also warned Labour is “in a hole” in Scotland and England and needed to appeal to traditional Labour communities plus the aspirational “John Lewis couple”.
Shadow health Secretary Andy Burnham is almost certain to run while the odds on shadow home secretary and Normanton MP Yvette Cooper lengthened over the weekend after her husband Ed Balls was voted out in Morley and Outwood. London MP David Lammy told a television interviewer on Saturday he would consider a bid while Leeds West MP Rachel Reeves is another potential candidate, although she has yet to state a position.
Former home secretary and Hull MP Alan Johnson ruled himself out of the running.
Meanwhile John Prescott, unleashed a blistering attack on the Labour campaign, pouring scorn on Mr Miliband’s “Hell yes, I’m tough” claim and accusing him of failing to defend the previous Labour government’s record on the economy.