Looking pale and drawn, the Deputy Prime Minister insisted it had not "crossed his mind" to resign, saying he "wouldn't hesitate" to do so if he thought it would help his party.
But Mr Clegg noted how four years ago the LibDems had made a commitment to repair the British economy and they "must finish the job".
He made clear it was right colleagues asked searching questions after such electoral losses but insisted when the going got tough, it would be wrong to walk away.
"Just at the point when…our big judgments are being vindicated, we're not going to buckle, we're not going to lose our nerve, we're not going to walk away," he declared.
The LibDem leader admitted his decision to go head to head with Ukip leader Nigel Farage had not been successful but it had been "right that we stood up for the values we believe in".
Senior colleagues rallied round.
Lord Ashdown, the former party leader, praised Mr Clegg's "extraordinary courage", saying: "I don't think it's helpful for us to either be distracted from the real issue ahead, which is the campaign for the General Election, nor is it right for us to be doing our enemies' work in this matter."
But perhaps the biggest support came from Vince Cable, often seen as a potential leader. On a trade trip in China, the Business Secretary made clear there was "no leadership issue" and called on the party to "hold its nerve".
Earlier, John Pugh, the MP for Southport, said he wanted Mr Cable to take over as leader, warning that voters' unwillingness to listen to Mr Clegg was a fundamental cause of the LibDems' "abysmal" showing.
His colleague John Hemming suggested Mr Clegg should consider his position while former MP Sandra Gidley warned that under the leadership the LibDem brand had become "toxic".
In contrast, Ukip held a victory rally with a beaming Mr Farage claiming his "people's army" was on its way to Westminster after the anti-EU party secured an historic victory in the European parliamentary elections, winning 24 out of 73 seats.
He said Ukip would "do our damnedest to try to pull off an even more spectacular result" in next week's by-election in Newark, which the Tories are defending with a 16,000 majority.
Earlier, David Cameron launched a personal swipe at Mr Farage, who has dubbed himself "the bloke from the pub who went to Strasbourg".
The Prime Minister said: "He's a consummate politician. We've seen that with his expenses and his wife on the payroll and everything else. So I don't really accept the 'he's a normal bloke down the pub' thing."
After stopping off for a celebratory pint in a local Westminster pub, Mr Farage announced he would unveil Ukip's draft election manifesto in Doncaster, saying: "It is a town in which Ed Miliband is the MP, it's a town in which yesterday we topped the polls, and we will have an honest conversation with the British public about the cost-of-living crisis and about how we can make life better and more affordable for ordinary families. Policy will happen in Doncaster in September."
The Labour leader, who is due to make a speech in Thurrock today, where Ukip has eaten into his party's stronghold, admitted its victory in the Euro poll showed there was a "desire for Europe to work better for Britain".
But he defied calls from veteran Labour MPs Frank Field and Austin Mitchell to pledge his own in/out referendum, stressing there would only be a poll if there was a further transfer of powers to Brussels.
Mr Miliband claimed Labour was making progress but added there was further to go, although he still believed the party can win the General Election.
Prime Minister David Cameron told EU leaders ahead of a dinner in Brussels tonight the importance of heeding the results. A Downing Street spokesman said he told them to "seize the opportunity to heed the views expressed at the ballot box that the EU needs to change and to show it cannot be business as usual. The turnout and results in the European Parliament elections have underlined the need for reform."