Liberal Democrats must show "unity and purpose" after Mark Oaten resigned over an alleged affair with a rent boy, said acting leader Sir Menzies Campbell.
A newspaper claimed the father-of-two, who quit as home affairs spokesman, had a relationship with a 23-year-old man.
The Winchester MP, 41, has apologised to his family and appealed for privacy.
Sir Menzies, leader since Charles Kennedy resigned, and fellow leadership candidate Chris Huhne both said the party was big enough to move on.
Mr Oaten's resignation from the party front bench came just weeks after Mr Kennedy quit as party leader after confessing to alcohol problems.
'Shocked and disappointed'
In a statement, Mr Oaten, who quit the leadership race on Thursday, apologised for "errors of judgement in personal behaviour" after the News of the World published claims he used a male prostitute.
Sir Menzies told Sky News: "I don't think one should be angry about these things. The task is to draw the party together and move forward.
"He and his family now need to have their personal privacy respected"
"No party is entirely subject to what happens to any one individual. The party is much bigger than that and my task as acting leader is to restore a sense of unity and purpose."
Mr Huhne echoed Sir Menzies, telling the BBC the implications of Mr Oaten's resignation for the party "should not be overestimated".
Mr Huhne also said he hoped to see Charles Kennedy back on the Lib Dem front bench in the future.
Edward Lord, Mr Oaten's election agent for the leadership campaign, said it was an "enormous shame" that the Lib Dems had lost him from the front bench.
He said Mr Oaten was "shocked and disappointed" with the way the story was handled and described him as "one of those timeless politicians of a generation".
'Reprehensible'
Lord Carlile, who has also served as home affairs spokesman for the party, criticised the News of the World for its style of journalism.
"He's a front bench spokesman who then went on to stand as a potential leader of the Liberal Democrat party - that is someone who quite clearly has a public life"
"If the newspapers were simple revealing fact, then I think one might find some excuse for them," he said.
"But all the News of the World wants to do is publish lurid detail - and I think that this is highly reprehensible conduct by the newspaper."
Keith Gladdis, Whitehall editor of the News of the World, defended the paper's story by stressing Mr Oaten was a public figure.
"Mark Oaten is an MP, an MP who has been elected on a platform of being a family man.
"He's also an MP who's a front bench spokesman - a front bench spokesman who then went on to stand as a potential leader of the Liberal Democrat party.
Leadership battle
"That is someone who quite clearly has a public life."
When standing down as a Lib Dem leadership challenger on Thursday, Mr Oaten said the remaining three contenders all "had much more support" among MPs.
His withdrawal left Sir Menzies, Mr Huhne and Simon Hughes as the remaining candidates.
Mr Oaten's deputy, Alistair Carmichael, has taken over temporarily as home affairs spokesman.
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