Former Labour MP John Mann said the leader's unpopularity on the doorstep was palpable and Mr Corbyn should have "gone already".
Lord Blunkett, a former Labour cabinet minister, called for the party leadership to apologise for the election defeat, adding that they were "lacking in any contrite belief that they made a mistake".
At 33%, Labour's share of the vote is down around eight points on the 2017 general election and is lower than that achieved by Neil Kinnock in 1992.
LIVE: Updates and reaction as results come in
Tories take Labour seats as they head for majority
Mr Corbyn said it was up to the National Executive, the ruling body of the party, to decide when he would go, adding it was likely a new leader would be selected in the early part of next year.
He said he would not step down as leader yet because the "responsible thing to do is not to walk away from the whole thing".
Asked whether he was part of the problem, he said: "I've done everything I could to lead this party… and since I became leader the membership has more than doubled and the party has developed a very serious, radical yes, but serious and fully-costed manifesto".
Image caption
Keir Starmer, one of the favourites to be the new leader, says it's "a big task" to rebuild Labour
Keir Starmer, one of the favourites to replace Mr Corbyn as leader, said there was "no hiding" from the election result which was "devastating for our party".
He said it was the party's duty to "rebuild" which was going to be "a very big task".
Asked if he wanted to be the next leader, he said: "I think this is the time for reflecting and understanding the result. I don't underestimate the size of the task ahead."
Unite union boss Len McCluskey, an influential Labour ally, said the result was "deeply, deeply disappointing" and the party had "failed" because it had tried "to go beyond Brexit".
"Unfortunately our Labour heartland who had voted Leave, they undoubtedly felt that Labour had let them down," he said.
"My worst fears have come true, it was always Labour's Achilles' heel."
The Conservatives took Labour strongholds across northern England, the Midlands and Wales in areas which backed Brexit in the 2016 referendum.
Some traditional Labour constituencies, such as Darlington, Sedgefield and Workington, in the north of England, have a Conservative MP for the first time in decades - or in the case of Bishop Auckland and Blyth Valley - for the first time since the seat was created.
Mr Corbyn was re-elected with a reduced majority of 26,188 as the MP for Islington North.
Reflecting on his party's defeat, My Corbyn said: "My whole strategy was to reach out beyond the Brexit divide to try and bring people together because ultimately the country has to come together."
The party promised to renegotiate Prime Minister Boris Johnson's Brexit deal, and put it to a referendum vote alongside the option of remaining in the EU.
Asked what went wrong for the party, he said: "Those in Leave areas, in some numbers, voted for Brexit or Conservative candidates which meant that we lost a number of seats and we didn't make the gains that I'd hoped we could have done".
Asked whether "Corbynism" is now dead, he said: "There is no such thing as Corbyninsm… there is socialism."
He added: "I don't think [socialist ideas] are unelectable."
Mr Corbyn said his party's policies were individually "very popular" and there was no "huge debate" about them within the party.
Dame Margaret Hodge, MP for Barking, said under Mr Corbyn's leadership, Labour had become the "nasty party", with anti-Semitism allowed to flourish.
Speaking about his party's handling of anti-Semitism, the Labour leader said: "I inherited a system that didn't work in the Labour party on anti-Semitism, I introduced the rule changes necessary to deal with it and they're in operation.
"Anti-Semitism is an absolute evil curse within our society and I will always condemn it and also do and always will".
Meanwhile, the rapper Stormzy, who backed Labour ahead of the election and described Mr Corbyn as "a man of hope", has told BBC Radio 1Xtra that the result feels like "a dark cloud".