The site has been relaunched, claiming it is no longer a "government mouthpiece".
In an interview with BBC News, Mr Draper said continuing as editor would have damaged the site and he would not have been able to persuade cabinet ministers to write for it.
Asked if he was ashamed by his actions, he replied "absolutely", adding that he deserved to be "held accountable".
He said there had been a "series of meetings" about setting up a Labour rival to popular right wing blogs such as Conservativehome, Iain Dale and Guido Fawkes but he said Red Rag was a "random idea" and "in terms of Damian's email no-one, as far as I know, in Downing Street or the Labour Party knew about it".
He added: "The idea of putting those horrible stories on to a website was wrong."
Explaining his motivation, he said: "I was slightly in awe of Damian McBride. I wanted him to be supportive of Labour List. I was wrong and I should lose out because of it'.
He said he would be quitting frontline politics as nobody would want advice from him now, saying: "I won't be doing much in politics -I will be leafletting in my ward, that will be the limit of my contribution."
He admitted his activities had been a problem for the prime minister and he urged fellow Blairites to rally round Mr Brown.
"I'm not sure anyone's best interests are served by people sniping at the guy who is likely to lead us into the next election."
He said he did not think Mr Brown got the credit he deserved for "sorting out the economy," adding: "Maybe as the election nears people will judge that, rather than looking at an email two idiots sent".
Mr Draper, a former aide to Lord Mandelson, was fired in 1998 after a "cash for access" scandal which saw him boasting to an undercover reporter, posing as a businessman, about his contacts with senior figures in the government.
He retrained as a psychotherapist and married the GMTV presenter Kate Garraway but made a surprise return to frontline politics at the end of last year, when he was recruited by Labour, in an unpaid capacity, to beef up its internet presence.
He launched the LabourList site earlier this year and the site initially carried pieces by Cabinet ministers, such as Lord Mandelson and Douglas Alexander, and other senior Labour figures.
But Mr Draper attracted controversy from the start and when Guido Fawkes obtained e-mails about plans to smear senior Tories, which led to the smeargate scandal, he was dropped by the Labour Party.
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