In evidence to the Culture, Media and Sport Select Committee, the Cabinet Office minister made clear he did not intend to follow the flamboyant role of his predecessor.
"I regard my role as shareholder, not as a micro-manager. It's not for me as shareholder to start fiddling around at the edges," he said.
During his term in charge of the Dome in Greenwich, southeast London, Mr Mandelson took a high-profile role in promoting it at home and abroad.
Lord Falconer said the project was still on schedule to meet its pounds 150m target for private investment, and had already raised more than double the previous government fund-raising record of pounds 60m for the Euro 96 football tournament.
The minister also confirmed that there would be no cable car ride to transport visitors to the Dome, a fact that was a source of "immense regret" to the Government.
In response to the Archbishop of Canterbury's claims earlier this week that he would boycott the Dome if it failed to have a significant Christian celebration, Lord Falconer insisted that the project's Spirit Zone was an integral part of the whole operation. "It is 2000 years from the birth of Christ. That must be appropriately marked at the end of the year. That's not to exclude other faiths," he said.
He dismissed a suggestion from John Maxton, Labour MP for Glasgow Cathcart, that the Dome should have no religious element because 1 January was not a significant date, unlike 25 December.
The head of the company behind the scheme earlier told the MPs that the millennium exhibition could be extended into 2001 if there was sufficient public demand.
Jenny Page, chief executive of the New Millennium Experience Company, said that she did not want to rule out such a suggestion.
"To get to the end of 2000 and still have an extra demand would have to be more than fantastic, it would have to be extraordinary. We would have to talk about whether a suitable extension would have to be made," she said.Reuse content