Corbyn said he will not lead the party into another election but pledged to carry on as Islington North MP and interim party leader.
He spoke as Labour faced electoral wipeout throughout the country, projected to win just 191 seats across the UK.
North of the border Ian Murray was set to be the sole remaining Scottish Labour MP.
Bookies make Keir Starmer the early favorite to take over as the next leader.Mr Corbyn said he will remain as MP for Islington North.
He said: "I want to say this, I will remain the MP for Islington North and I'm proud to represent the people of Islington North."
He added: "And I'm proud in Parliament and outside that we will forever continue the cause for socialism, for social justice and for a society based on the needs of all rather than the greed of a few.
"That is what makes our party what it is and I'm very proud of the achievements of our party and the development of its manifesto and its ideas.
"I tell you what, those ideas and those principles are eternal and they will be there for all time."
Boris Johnson held onto his Uxbridge seat with a majority of more than 7,000, and said it "looked as though this One Nation Conservative government has been given a powerful new mandate to get Brexit done".
Mr Corbyn's party, which had 243 MPs when Parliament was dissolved last month, is forecast to lose 52 seats, according to a BBC/Sky/ITV exit poll, which put the Tories on 368 seats.
The poll predicted Labour would win just 191 seats, the Scottish National Party 55, Liberal Democrats 13, the Brexit Party none, Plaid Cymru three and Greens one - giving Mr Johnson a majority of 86.
Such a poor result would be the worst for Labour in terms of seats since 1935.
However, they clung onto several North East seats including Newcastle Central, Sunderland Central, Newcastle-upon-Tyne East and Houghton and Sunderland South, but with much reduced majorities - and won Putney from the Tories.
The first results chimed with the exit poll prediction, as support for Labour slumped in its Brexit-voting heartlands.
In the biggest scalps of the night so far, DUP Westminster leader Nigel Dodds - whose party propped up Theresa May's administration - lost his Belfast North seat to Sinn Fein.
And former Tory minister Zac Goldsmith lost to the Lib Dems in Richmond Park.
For Labour, the first big upset came as the Tories won Blyth Valley with a 10% swing from Labour - a seat they had held since 1950.Shadow environment secretary Sue Hayman lost Workington on another 10% swing to the Tories and former minister Caroline Flint lost Don Valley.