He said he hoped it showed the party had changed "into a party that can be trusted after 30 years with the greatest, most cosmopolitan, multi-racial generous hearted city on earth".
Mr Livingstone's defeat ended what Gordon Brown called a "bad" day for Labour, in which it suffered its worst council results for 40 years.
Asked by the BBC what his views were on the poor Labour showing, Mr Johnson said: "The smart thing for Labour to do would be to quietly to remove Gordon Brown and install [Foreign Secretary David] Miliband, is my view, but I don't think they'll do it."
In his speech after the result was declared at City Hall, Mr Livingstone thanked the Labour Party for all its help with his campaign.
Ken Livingstone accepts electoral responsibility
"There is absolutely nothing that I could have asked from the Labour Party that it didn't throw into this election, from Gordon Brown right the way down to the newest recruit, handing out leaflets on very wet, cold days.
"I'm sorry I couldn't get an extra few points that would take us to victory and the fault for that is solely my own. You can't be mayor for eight years and then if you don't at third term say it was somebody else's fault. I accept that responsibility and I regret that I couldn't take you to victory."
However, Justice Secretary Jack Straw said Labour as a whole should shoulder the blame for Mr Livingstone's loss.
He told BBC News: "I disagree with Ken in one particular only, that we all share the responsibility for the defeat that he suffered yesterday."
Mr Straw admitted that the row over the 10p tax rate had left some voters "understandably very upset".
The government would get behind Londoners' decision at the polls, he added.
Conservative Party leader David Cameron praised Mr Johnson for a "serious and energetic campaign" and said his party was "winning the battle of ideas".
David Cameron celebrates as Johnson's win is announced
Liberal Democrat candidate Brian Paddick paid tribute to Ken Livingstone as "an amazing mayor" and indicated that he would not be interested in working with Mr Johnson.
He said he would be talking to Lib Dem leader Nick Clegg about his future and what he could do for the party.
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