John McDonnell has defended Labour’s decision not to fully endorse a second EU referendum so far, but acknowledged the party is going to get “a good kicking” in the European elections.

The shadow chancellor said he understood the frustration of Labour’s remain supporters, after Tom Watson, the deputy leader, criticised the party’s “mealy-mouthed” approach to backing a second referendum.

But he said Labour could not have simply ignored the people who voted to leave the EU. Instead, McDonnell said it was right to have chosen the “hard road” of trying to please both leavers and remainers, as Labour wanted to bring the country together.

“We’re a strong remain party but we couldn’t ignore that 52% voted leave, we can’t turn our back on those people,” he told Sky’s Sophy Ridge on Sunday.

McDonnell acknowledged that the European election results were likely to be difficult for Labour, which may come third amid a surge in support from remainers for the Liberal Democrats and Green party.

“I think we most probably will get a good kicking in the election results tonight,” he said. “We’ll see. We’re braced for that. But we had to do the responsible thing … I know it was hard and it was difficult. It was a hard road to follow. But someone had to be there and say: ‘Can we bring the country back together again?’”

McDonnell struck a conciliatory tone towards Watson, but said: “It would have been easy to go to one side, you know, to the remain side and ignored all those people who voted leave.

“That’s not the nature of our party. We’re the party that is trying to bring people back together again. That’s been difficult, electorally, for us in these elections. Of course it has. But now we’ve got to move on.”

He hinted that Labour could in future move to unequivocal backing for a second referendum as a way of stopping a no-deal Brexit.

“There is real threat now of an extremist Brexiteer becoming the leader of the Conservative party and taking us over the cliff edge of a no deal,” he said, saying Labour was seeking to work with other opposition parties. “We have got to move forward now, bring people together and block a no deal and if that means going back to the people, so be it.”

Before the European results were due to come in on Sunday night, Watson, in an article for the Observer, delivered a critique of Labour’s lack of full support for a second referendum.

Watson said: “Our performance is a direct result of our mealy-mouthed backing for a public vote on Brexit when it is being demanded loud and clear by the overwhelming majority of our members and voters.

“Polls show Labour has been losing up to four times more voters to parties giving full backing to a people’s vote than to Farage. And those same polls show we would have beaten him by a country mile if we had unambiguously backed a public vote on any form of Brexit.

“Once results are in, we must channel our frustration into winning those voters back. Never again can Labour policy on the most crucial issue of our generation be on the wrong side of its members and voters.”

Watson was backed by Shami Chakrabarti, the shadow attorney general, who said it had been right to say the democratic result of the EU referendum should be carried out but a second one was needed to break the deadlock.

She told BBC One’s The Andrew Marr Show: “I was a passionate remainer but I also am a democrat and wanted to listen to the 52%. However, a confirmatory vote or a second referendum now we are in the future is a way of breaking the deadlock in our country. It is not a means of stealing Brexit from those who voted for it. It has been part of our policy since party conference last autumn. It is past midnight. So that means of breaking the deadlock is more and more important by the day.”

Chakrabarti also said it would be extremely important to stop a no-deal Brexit by any means possible, as several of the leading Conservative leadership candidates are pledging to leave the EU at the end of October whatever happens.