The former business secretary said the lack of an alternative to Chancellor George Osborne's Northern Powerhouse was a "huge political mistake".
He said Labour did not have election policies to "rebalance both the economy and the political system".
In May, Mr Osborne said northern England would get more powers.
He laid out plans to transfer powers on housing, planning, transport and policing.
Lord Mandelson said Labour's proposals had not been "radical enough".
"We stepped back and passed the ball to the Conservatives and the coalition," he told BBC's Sunday Politics North West.
"And what did they do? They ran with it... and it was a strong part of their appeal both in the North West but also nationally.
"And the Labour Party, I'm afraid, has a long way to catch up. But catch up, it must do."
He added: "I think George Osborne got it.  I think he got it because he saw an electoral advantage in it... and we let him do so. And that was a huge political mistake."
Lord Mandelson, a key figure in the governments of former prime ministers Tony Blair and Gordon Brown, is currently running for the position of University of Manchester chancellor.
He has been nominated alongside writer Lemn Sissay and Sir Mark Elder from the HallÃ© Orchestra.
Lord Mandelson said he wanted the post "because the city of Manchester is becoming the most exciting, edgy place to be around in England".
"Let's be honest, something very exciting is happening in this region as part of the Northern Powerhouse."
The new chancellor will be announced on 22 June.
Sunday Politics North West, BBC One North West, Sunday 7 June 11:35 BST
During the General Election campaign Labour told voters its policies on devolution were more radical than George Osborne's "Northern Powerhouse".
But the trouble was nobody could point to a coherent strategy.
Lord Mandelson has become the first senior Labour Party figure to admit it simply did not exist.
The former business secretary was clearly frustrated policies he began to formulate in government were not developed by Labour in opposition.
He clearly believes the party handed a political advantage to the Tories, something he describes as "a huge political mistake".
No wonder so many North West council leaders have been willing to work collaboratively with the government, despite the substantial cuts they have endured.
It is difficult to imagine how Labour lost the political initiative in its own regional heartland.
Labour will fight hard to win it back but that will become increasingly difficult if the Northern Powerhouse strategy starts to bear fruit.
Lord Mandelson has criticised Labour for failing to come up with a credible strategy for decentralising power from London to northern England.