The shadow chancellor said “if anyone’s to blame, it’s me, full stop”, but also cited Brexit and the media for having “demonised” the Labour leader ahead of the dismal defeat.
Mr Corbyn’s key ally was speaking on Sunday as the post-mortem examination was in full swing, with potential candidates to replace the leader setting out their stalls.
Key figures in the current leadership were tipping shadow business secretary Rebecca Long-Bailey, but backbenchers Lisa Nandy and Jess Phillips were testing the waters for a challenge.
Ms Nandy said on Sunday morning she is 'seriously considering' running as a candidate.
Could Labour elect one of these MPs as its first female leader?
Mr McDonnell followed the outgoing leader in apologising for losing dozens of seats across the North and the Midlands to the Tories on Thursday, which saw Labour’s worst result since 1935.
“It’s on me, let’s take it on the chin, I own this disaster so I apologise to all those wonderful Labour MPs who have lost their seats and who worked so hard,” Mr McDonnell told The Andrew Marr Show on the BBC.
He also said he does “blame the media” which he said “demonised” Mr Corbyn “for four years solid, every day”.
He predicted the leadership change will take place in eight to 10 weeks, tipping Ms Long-Bailey as having the ability to be “a brilliant leader”.
Mr McDonnell also praised shadow cabinet ministers Angela Rayner, Dawn Butler and Richard Burgon, who himself was backing Ms Long-Bailey and said he is “considering” running as her deputy.
The shadow chancellor said he “prefers others” to Ms Phillips, before describing her as “really talented”.
He said the next leader should be a woman – which would make her the first to lead the party – and said it was “most probably time for a non-metropolitan” candidate as he said “we need a northern voice”.
Meanwhile Labour's Richard Burgon has admitted that the party's position on holding another EU referendum "did fail".
The shadow justice secretary, a key ally for outgoing leader Jeremy Corbyn, blamed Labour's catastrophic defeat on it being the "Brexit election" and defended the party's socialist manifesto.
On Labour's Brexit position, he told Sky's Ridge On Sunday:"I think it was right to attempt to bring the country together on that basis. Did it fail? We've got to be open, it did fail.
"It was a disastrous election result and for that we are truly sorry."
He criticised the Sun and Daily Mail newspapers for conducting a "character assassination" against Mr Corbyn.
"I think the biggest mistake the Labour Party made was perhaps underestimating the desire for people who had voted Leave to leave the European Union," Mr Burgon added.
He backed shadow business secretary Rebecca Long-Bailey to replace Jeremy Corbyn as leader and said he is "considering" running as her deputy.