Third place candidate Simon Hughes has congratulated new Liberal Democrat leader Sir Menzies Campbell and offered him his "full support".
Mr Hughes said the party had "a great future".
Asked if the result marked the end of his own leadership ambitions, the Lib Dem president told BBC News 24: "It is never the end of Simon Hughes".
He said he would carry on campaigning for a "more Liberal Britain".
And he told party members, who voted Sir Menzies and Chris Huhne ahead of him, it had been a "good campaign".
Sir Menzies has an "absolutely clear, unqualified, principled voice for liberal democracy", he added.
Mr Hughes also praised Charles Kennedy, who beat him to the leadership in 1999.
Speaking from the platform, he told Mr Kennedy - who was forced to resign earlier this year after admitting he had a drink problem: "You have given us a phenomenal start, but we haven't stopped now."
Mr Hughes, MP for North Southwark and Bermondsey, was knocked out in the first round in the ballot among the party membership, after coming third with 12,081 votes.
The voting system used for the election meant that after the first round, Mr Hughes' backers' second choices were transferred to Sir Menzies or Mr Huhne.
Sir Menzies won the second ballot with 29,697, with Mr Huhne in second place with 21,628.
In spite of his own defeat, Mr Hughes cheered Sir Menzies convincing win as "a truly Olympic victory".
He told Sir Menzies: "I have no doubt at all that under your leadership we will be a clear, united and successful party and ... you have my complete and unqualified support as I know you will do for the whole party."
He said Sir Menzies, the former foreign affairs spokesman was "respected at home and abroad".
And as for the Liberal Democrat party, he said it would be "safe in your hands" and told members the party had "a great future".
"I am absolutely clear that liberal democracy has a great future; and I am absolutely clear that we will go, Ming, under your leadership from strength to strength towards the government that Britain desperately needs and that we are all so unitedly determined to achieve."
He said the contest - which saw him admitting to having both gay and heterosexual relationships after repeated media questioning - was "a really good leadership election campaign".
Sir Menzies won the leadership contest after gaining 57% of the vote and said he was ready to take risks to "modernise" the party and lead it "back to government".