A grim-faced Nick Clegg has made clear he will resist calls to resign, saying the Liberal Democrat party he leads will not buckle or lose its nerve after a poor showing in the European elections.

Looking dejected and exhausted during a television interview, the deputy prime minister said he was determined to continue his work in government and resisted calls for a change in direction.

The last of the party leaders to respond to the European results, Clegg said: "Just at the point when our decisions, our big judgments are being vindicated, we are not going to buckle, we are not going to lose our nerve and we are not going to walk away."

He said he would resign if it would help the party but, insisted the right course was for him to stay on. The Lib Dem backbencher John Pugh has called on Clegg to make way for the business secretary, Vince Cable.

Clegg's aides had organised a carefully controlled media appearance after the Lib Dem share of the vote halved in the European elections to just under 7%, with the party finishing in fifth place behind the Greens. In a blow to Clegg's authority, just one Lib Dem MEP was elected – a fall of 10 on the last European elections in 2009.

Clegg recorded one television interview, with the BBC's Vicky Young, which was pooled among all broadcasters. It aired first on Sky News.

He said he accepted that many people had serious questions about his leadership. "I don't begrudge any individual for raising searching questions, asking challenging questions about strategy and about leadership. It is the most natural thing in the world after the electoral losses of the last few very, very difficult days."

But he said resigning would be the easy route. "If I'm honest with you, the easiest thing in politics – just as in life – is when the going gets really, really tough is just to walk away, to wash your hands of it. But I'm not going to do that and my party's not going to do that because we said in 2010 we were going to do something exceptional which was to enter a coalition for exceptional reasons – to deliver the economic recovery which has finally been delivered."

The deputy prime minister denied that he had a bunker mentality. "I am never going to put myself ahead of the Liberal Democrats, in the same way that we as a party are never going to put ourselves ahead of the interests of the country. If I thought that anything would be really solved, any of our real dilemmas would be addressed by changing leadership, changing strategy, changing approaches, bailing out now, changing direction, then I wouldn't hesitate advocating it. Absolutely not," he said.

"But I genuinely believe that at precisely the time that our big judgments have been vindicated – people said we had to switch to Plan B – again and again and again we held our nerve and we proved to make the right judgments. That is the worst point, in my view, to change direction."

Clegg won important support from Cable, who described the results as "exceptionally disappointing" but said it would be wrong to engage in "infighting and introspection".

In a statement issued from China, where he is leading a government trade mission, Cable said: "These were exceptionally disappointing results for the party. Many hard-working Liberal Democrats, who gave this fight everything they had and then lost their seats, are feeling frustrated and disheartened and we all understand that.

"Nick did a bold thing in standing up to the Eurosceptic wave which has engulfed much of continental Europe. We are the only party to have taken that on and he personally deserves tremendous credit for that. There is no leadership issue. We have also undoubtedly taken a kicking for being in government with the Conservatives and having to take some extremely tough decisions in the national interest. But now is not the time for infighting and introspection. The party must hold its nerve. We must focus on delivering our policies in government and that's exactly what I'm doing in China, helping British businesses secure contracts with the world's fastest growing economy."

Earlier, Pugh, the Lib Dem MP for Southport, told the BBC: "My personal preference would be for a Cable succession but that is not up to me. It's up to what the polls tell us about what will make the Liberal Democrats popular and successful and progressive. It is also what the party wants. We have to consider it. We can't just carry on as usual. If we carry on as usual we are exactly like the generals in the Somme because these losses are horrendous.

"We've got to keep our heads but given these circumstances – where we have lost 91% of our Euro MPs, we have come after the Greens in the Euro elections and we have lost a huge number of councillors – if we are not going to have a review of strategy and leadership, in whatever circumstances would we have a strategy review?

"Decide it [the leadership] now, decide it quickly. Given the scale of the losses – to call for business as usual is, frankly, ludicrous. We genuinely have to reflect very hard, very quickly, made some good decisions and get on to the 2015 election in better shape."

In a sign that unease is spreading to normally loyal MPs, Sir Nick Harvey, who was sacked as a defence minister in a reshuffle in 2012, called on the party to put more distance between the Lib Dems and the Tories.

Harvey told The World at One on BBC Radio 4: "There is a perception on the part of voters that we have got ourselves too embroiled with the Conservatives. When they look at things like the NHS changes, Michael Gove out on adventures in the education field; when they look at some of the more draconian benefit cuts, people are asking themselves if there is a point having the Lib Dems in the government. Surely it is to stop some of these things happening.

"We must be willing to say no to the Tories more. When you have a coalition between a larger party and a smaller one it is difficult for the small party to make the larger party do things it doesn't want to do. But it should be relatively easy to stop it from doing things we don't want it to do. That does mean that we need to be more willing to say no."

Harvey added: "We've just got to spend the next year showing clear water between ourselves and the Conservatives and what it is that we stand for that is different. I am not sure, despite the fact that there are great achievements from the last four years, that we have really got quite enough distance between ourselves and the Conservatives. That's what's enabled Labour and the Greens to profit at our expense."

The leadership appeared to acknowledge on Monday afternoon that an initially aggressive response to the internal critics may have backfired, as the former Lib Dem leader Lord Ashdown adopted a rare humble tone.

The party's general election co-ordinator, who had threatened to use his military skills to deal with critics, told The World at One: "I feel, as I think everybody else does, the deepest pain for those really outstanding councillors and MEPs who have bravely fought for their communities, for the things they believe, and the things they believe are right for Britain and have not been elected. It is a hard night for us.

"But here is the point. The strategy of the party has been, and remains, to sit out the mid-term elections and all the pain they involve – and deep, deep pain last night, more than we'd imagined would be – for what happens next. What happens next is the opportunity to put forward our case for our actions in coalition government in the context of the general election."