Lib Dem federal executive member Martin Tod directed his anger towards Clegg and the party leadership at chief secretary to the Treasury Danny Alexander live on the BBC.
"They [voters] are not prepared to listen to our leader and thats a really serious problem and it is a problem we need to address," he said.
Asked by David Dimbleby whether ditching Clegg would look like "panic", Tod said it would look like "listening to the electorate".
"You can't lose all of your MEPs, bar one, and pretend that nothing has happened, that your strategy is perfect and you just need to carry on as you are. We've been doing this year after year after year. We keep being told it's a the mid-term and the mid-term moves nearer and nearer every year to the date of the general election. I'm extremely concerned.
He added: "I'm really concerned if we stay with Nick and stay with the current strategy we will get the result that this year has told we will get in next year's general election."
Alexander, who sat motionless and ashen faced as Tod spoke, insisted he was concerned by the results but it would be wrong to try and oust Clegg.
"I don't think plunging the party into a period of introspection is the right answer to that. I think Nick Clegg has done a fantastic job as our leader and as deputy prime minister."
Lib Dem party president Tim Farron said Clegg, who is facing calls from some activists including general election candidates to step down, should be praised for having the "backbone" to take an unpopular position over the EU and confront Ukip's "threat to British cultural values".
Clegg's future was already being questioned by MPs as would-be MPs in target Westminster seats joined voices urging him to fall on his sword over the dismal performances.
Farron told Sky News: "Britain is a diverse country, it is a country where we stand up for civil liberties, it is a country where we recognise that our national interests are in being part of the European Union.
"Someone has to have the backbone to stand up and say that. It looks like we may have paid the price but I would do it all again. Being unpopular is not the same as being out of touch. We understand what the British people think and we understand that on this issue we've taken the unpopular side of an argument."
Clegg has insisted he is staying despite the party losing more than 250 councillors in local elections and being humiliated in the European elections.
Catherine Bearder, the Liberal Democrat's only remaining MEP, stayed loyal to her party leader and said Clegg had been right to go out and campaign on a positive EU platform.
She told Sky News: "It's been very difficult. We are in government so there is always a chance to squeeze and that happens in politics. We fought a very good, positive campaign on our issues of being in the European Union and standing up for Britain in the European Union."