The ex-home secretary said the decisive 62% victory for the veteran left-winger, who saw off a challenge from Owen Smith on Saturday, was an “utter disaster” and urged moderates to fight to take the party back.
But close Corbyn ally John McDonnell said Lord Blunkett was “completely out of touch” and called on him to respond to the leader’s call for unity.
The shadow chancellor was due to use a keynote speech to Labour’s annual conference in Liverpool to announce plans to form an “interventionist government” borrowing £100 billion at low rates to support British industry.
Mr McDonnell told ITV1’s Good Morning Britain: “David has been fairly critical of Jeremy all along, but I’m sure he will calm down.
“There is a real spirit here of people getting together and uniting and thinking that we may face a general election soon so we have to get our act together to form not just a good opposition but to get ready to go into government.”
Mr McDonnell was speaking after the opening day of the conference saw moderates pack rallies of the Labour First and Progress movements to hear a string of centrist MPs warn that the party could die unless it changes course.
And Lord Blunkett told the Daily Mail: “For the Labour Party I love, the party I have devoted more than 50 years of my life to serving, the re-election of Jeremy Corbyn as leader is a catastrophe.
“I’m in despair at this calamitous situation. I honestly cannot see how we’re going to get out of it.”
Denouncing Mr Corbyn’s supporters as Marxists who were “disconnected from the broad electorate”, Lord Blunkett said: “The Labour Party under Corbyn is not electable. I am at a loss to understand what the 313,000 members who voted for him believe they can really achieve in the next three years, and what the eventual outcome will be, other than annihilation at a general election in 2020.”
But he cautioned Corbyn critics not to split the party, warning that setting up “an alternative movement to seize the middle ground” would be “doomed to failure”.
Conference was due to hear from shadow foreign secretary Emily Thornberry that Labour will guarantee to make up any shortfalls in funding for deprived regions and communities resulting from Britain’s departure from the European Union.
Chancellor Philip Hammond has promised to continue the support until 2020, but Ms Thornberry was telling conference that this does not go far enough. She will promise a fully-protected fund to substitute for the lost EU money stretching further into the future.
Meanwhile, the shadow chancellor was using his keynote speech to herald a post-Brexit “manufacturing renaissance” backed by a comprehensive industrial strategy under Labour.
And wrangling continued in Liverpool over proposals to appoint Scottish and Welsh representatives to the party’s ruling National Executive Committee.
It is understood that Mr Corbyn is resisting moves to allow the party’s leaders in Scotland and Wales to appoint their nominees and pushing instead for them to be chosen by members.