Erik ten Hag admitted Manchester United “got away with it” after they somehow survived an epic Coventry comeback from 3-0 down to seal victory in the penalty shootout and set up a rematch of last year’s FA Cup final against Manchester City.

United appeared to be cruising towards an easy victory when Bruno Fernandes added to first-half goals from Scott McTominay and Harry Maguire just before the hour mark. But having opted to withdraw the outstanding Kobbie Mainoo from midfield, Ten Hag watched on in horror as Coventry hit back through Ellis Simms and Callum O’Hare before Haji Wright’s added-time penalty took the game to extra time.

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Both sides hit the woodwork before the Coventry substitute Victor Torp had what he thought was a late winner ruled out by VAR after Wright was adjudged to have been marginally offside in the buildup. But after Casemiro had missed the first penalty in the shootout, failures from the spot by O’Hare and the Coventry captain, Ben Sheaf, eventually allowed United to prevail.

Having dominated the match until the 70th minute, Ten Hag – whose position as manager is likely to come under increasing scrutiny after allowing another lead to slip – acknowledged that his team had been fortunate to scrape through, with United’s owners Joel Glazer and Sir Jim Ratcliffe watching on from the stands.

“We can’t say this group doesn’t have the right mentality because they showed character today, but in the final part there was a lack of discipline,” said the United manager. “It’s about communication and we have to improve on this.”

Asked why his team have struggled to hold on to leads this season, Ten Hag added: “We can play at a very high level but at the same match we can drop to very low levels. It is not explainable but it’s about taking responsibility. I have to teach my players and we have to do better. On several occasions we have let the results slip away but today we got away with it. I see the mistakes but it’s not an embarrassment – to reach the FA Cup final again is a huge achievement and we will take energy from this.”

The United goalkeeper André Onana saved O’Hare’s weak penalty in the shootout but was frustrated that his side had “lost control of the game”. “It’s a mixed feeling – we were in control but after so many individual mistakes we conceded three goals,” he said.

The Coventry manager, Mark Robins, was justifiably proud of the Championship side’s effort against his former club but admitted it was a hard defeat to take after also losing on penalties to Luton in last year’s playoff final.

“Had he cut his toenail, it wouldn’t have gone to penalties” he said of Wright for Torp’s disallowed goal. “You don’t get a chance often to go to an FA Cup final and we were really, really close. We started to play when it was 3-0 down and ended up really putting the pressure on United. I’m really proud of everybody – our players and supporters have been amazing throughout this FA Cup run. We’ve just said to them they’ve put themselves right up there in the history of the football club. People will talk about this game for a long time. We can’t feel sorry for ourselves.”

United were beaten 2-1 in last year’s final by City as Pep Guardiola’s side went on to claim the treble. But Ten Hag, who is hoping to add to last season’s Carabao Cup triumph in his second season at Old Trafford, believes they can go one better this time.

“I’m sure we have a good chance, although we play the best team in the world,” he said. “We’ve had a lot of injuries and hopefully those players can be back for the final. If we go with a squad who believes then we have a chance to win a trophy.”