A sharp split has emerged between the two chief architects of Labour’s Brexit policy as John McDonnell and Keir Starmer delivered vastly different verdicts on how their strategy affected the party’s performance in December’s general election.

McDonnell, the shadow chancellor, who is said to have convinced Jeremy Corbyn to back a second referendum, said in an exclusive interview before the budget that the party had been caught in a “vice” trying to please voters and members. The Tories had a simple message that was “unchallengable”, he suggested.

Starmer, the shadow Brexit secretary, said in a separate interview that their policy was right and it was not the sole reason the party suffered its worst election defeat since 1935.

McDonnell’s intervention is the first time he has given such a frank assessment on the policy he helped devise and how it may have ultimately hit Labour at the ballot box. He said the party should now drop the issue for a generation and accept that Brexit was happening.

“The reality now is Brexit is going to happen. It’s can we get a Brexit that at least protects jobs and the economy. And can we establish a new relationship with Europe,” he said.

McDonnell will retire to the backbenches when a new Labour leader is elected, and one of his first jobs then will be to establish connections with socialist parties in the EU to see how they can agree a policy programme for the future of the left in Europe without Britain in the EU.

Days before voters went to the polls, McDonnell said he thought Labour’s plan would stop Brexit supporters flocking to the Tories. He claimed the party would negotiate a “credible and sensible” withdrawal agreement with the EU within three months of forming a government, and then put that deal to a referendum within six months.

In that scenario he would have campaigned for remain, and he was part of a powerful clique in the shadow cabinet alongside Emily Thornberry, the shadow foreign secretary, and Diane Abbott, the shadow home secretary. However, he admitted in his interview: “You can’t buck democracy.”

McDonnell said: “We were caught in a vice. And the vice was between do we go for a full remain and lose more leave seats, or do we go for full leave and lose remain seats?”

He suggested the party would have succumbed to a 150-seat Tory majority had it not struck upon a policy that straddled both viewpoints. He claimed the party managed to pull back votes from the Liberal Democrats while attempting to retain Labour leave voters with stronger policies on NHS funding. The Tory majority in the end was 80.

McDonnell said it was not possible to tell for certain whether advocating for a stronger leave position would have produced a different outcome. “If people think that’s their number one issue, what better can you offer them than that hard simple message from the Tories and the Brexit party, which was unchallengeable in that sense,” he said.

On Sunday Starmer confidently backed the policy he helped negotiate and said he would have gone further and pushed the leadership to tell members which side they would campaign for.

Asked on the Sophy Ridge on Sunday show on Sky News if it was the right policy, Starmer said: “Of course.” He said: “I thought it was the right policy. I thought we should have gone on by the way and said which side we would be campaigning on if there was a referendum and I warned our party that if we looked indecisive, we wouldn’t look like we were leading on this issue.”

He said going into an election saying Labour would try to get another deal was the right thing to do because Boris Johnson’s proposals “would be very damaging for our country”.

Other members of the shadow cabinet have said since the election defeat that they repeatedly warned the party not to back another referendum on Brexit and to lean more towards their leave-supporting voters.

The shadow cabinet secretary, Jon Trickett, said the policy was a mistake while the party chair, Ian Lavery, said Labour ended up trying to “foist” a remain position on working-class communities.

Starmer said Brexit was only one of several reasons for Labour’s election loss. He said: “I think we all take responsibility for that devastating election loss. People brought up the leadership of the Labour party, fairly or unfairly; they brought up Brexit in different ways – what was said in the Midlands was different to what was said here in Scotland; they brought up the fact that they thought the manifesto was overloaded and they didn’t believe we could deliver it all; and in a number of places they brought up antisemitism.”

Starmer, Lisa Nandy and Rebecca Long-Bailey are through to the final stage of the Labour leadership contest, where members are balloted on whom they want to succeed Corbyn.