Mr Collins denied any knowledge of the e-mail campaign
The row over Labour smears has been "resolved" and ministers must focus on other issues, Lord Mandelson has said.
Reports that the Labour Party's general secretary met the men caught up in the smear campaign row to discuss online strategy were "tittle-tattle", he said.
Ray Collins met Damian McBride and Derek Draper a month before the e-mails - smearing leading Conservatives - were sent, the News of the World reported.
The Conservatives said the culture of how No 10 operated must totally change.
Shadow chancellor George Osborne, one of the victims of the smears, told the BBC's Andrew Marr show that Gordon Brown must be "held to account" for how people around him behaved.
Lord Mandelson: "The government has got to concentrate on its job"
Senior Labour figures have admitted Mr McBride's decision to send e-mails to Mr Draper containing lurid and unfounded claims about several senior Tories caused serious damage to the party.
Lord Mandelson said Mr McBride should not have been surprised by the outcry over his actions and that the prime minister had acted "so decisively and quickly in getting rid of him".
This issue has been resolved and the public wants us to focus on their concerns
He told BBC Radio 4's World This Weekend programme that the saga had ended with Mr McBride's exit.
Lord Mandelson said the story concerning Mr Collins was "going precisely nowhere" and he had nothing to answer for.
Mr Collins admitted being at the meeting with the two Labour aides but said he had "no knowledge whatsoever of any smears".
Asked about Mr McBride's e-mails, Mr Collins has said he "found the stories and reports of the last week absolutely disgusting".
Mr Collins said his meeting with Mr McBride and Mr Draper took place at the premises of the union Unite in December, after the Red Rag website at the centre of the scandal was set up.
George Osborne on personal smears against political opponents
Mr Collins said it was to "discuss online digital campaigning and how we could support and encourage left-of-centre websites and bloggers".
He added: "This meeting was not about scurrilous rumour, personal attacks or smears, as I would have been furious that such things could be seen as legitimate tools of political debate. As the PM has made clear, there is no place in politics for this kind of activity."
His version of events has been backed up by Kevin Maguire, associate editor of The Daily Mirror, also present at the meeting.
Mr Brown personally apologised for Mr McBride's actions while making clear that neither he nor any other minister knew of what Mr McBride was doing.
Lord Mandelson said the matter was now closed and no-one in government was implicated in Mr McBride's dealings.
"That is where the matter, I believe, can rest."
With the Budget days away, Lord Mandelson said ministers should not be "distracted" from the important tasks facing them.
But three separate polls in Sunday's newspapers suggested Labour's support was being affected by the smears row.
A third of those questioned in a BPIX survey for the Mail on Sunday thought Gordon Brown's government was sleazier than the last Conservative administration - compared to 23% who said it was less sleazy.
The Conservatives say the meeting involving Mr Collins "suggested" knowledge of a potential smear campaign against them extended beyond Mr McBride.
"Gordon Brown has to live with the regime he runs out of Downing Street," Mr Osborne said, describing the attacks on him and his family as "very unpleasant and particularly personal".
"Gordon Brown is responsible for the culture he creates in Downing Street. That culture has to end."
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