The 20-time English champions led 3-0 at Wembley with 58 minutes on the clock, with Scott McTominay, Harry Maguire and Bruno Fernandes on the scoresheet.
Coventry staged an incredible comeback to level it up at 3-3 in the final 20 minutes and force extra-time, and they appeared to have won it in the final stages when Victor Torp registered from close range.
However, the offside flag saved the Red Devils, and they went on to win the penalty shootout 4-2, with Diogo Dalot, Christian Eriksen, Fernandes and Rasmus Hojlund scoring after Casemiro had missed their opener.
Ex-Man United captain Roy Keane has claimed that Man United «looked like a Championship side» rather than Coventry, who operate in the second tier of English football.
Roy Keane critical of Man United after late capitulation«Coventry looked like a Premier League team and Manchester United looked like a Championship side,» Keane told ITV Sport after the extraordinary semi-final in the English capital.
«The Manchester United players and supporters weren't going over the top because they were lucky to win. They were almost embarrassed in the end.
»I don't like what I see when I watch this United group. I don't see leaders. They give up chances, they give up goals, we've seen it all season and they rode their luck today."
Fernandes also admitted after the match that it was difficult to be too pleased with the outcome, with Man United's standards dropping this season after a positive first campaign under Erik ten Hag.
«When they scored a goal [in extra time] we thought it might be offside, we couldn't
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