Erik ten Hag said Manchester ­United’s FA Cup victory against ­Liverpool could be the turning point he and his team need after beating their fierce rivals in an epic ­quarter‑final at Old Trafford.

United came from 2-1 down in normal time and 3-2 down in extra time to win 4-3 thanks to Amad Diallo’s 120th‑minute winner. The matchwinning substitute was sent off for removing his shirt during the wild celebrations, having been booked earlier for preventing a quick ­Liverpool free-kick.

Related: Manchester United edge Liverpool in FA Cup thriller as Amad Diallo strikes late

Ten Hag’s team could have completed their comeback in normal time only for Marcus Rashford to miss a gilt-edged chance with the final kick but, having booked a semi-final place against Coventry at Wembley, the United manager was thrilled with the character and desire on display at Old Trafford.

“It could be [a turning point] but we have missed so many opportunities,” Ten Hag said. “Arsenal in the fourth game of the season we should have had a penalty in the 87th ­minute, then we scored with ­Garnacho and it was disallowed and then we conceded a goal that should be disallowed. Every team needs these moments in a ­season but we never had one. This could be the moment that gives the team energy and the belief that they can do amazing things. When you can beat Liverpool like this you can beat any opponent.”

The United manager believes his side produced their best ­football of the season at the start of the ­quarter‑final only to lose their way as Liverpool recovered with goals from Alexis Mac Allister and Mohamed Salah. “The first 35 minutes we showed again that the future of this team is very bright,” he said. “There is huge potential and now we have to get it out con­sistently. The first 35 minutes was very pleasing. It was really fun to be part of this game. After the first 35 we had our drop and allowed them back in the game. We know they have a very good team but we showed resilience and determination to win the game.”

Defeat ended Liverpool’s dreams of a quadruple in Jürgen Klopp’s final season. The mana­ger said his side toiled in extra time when the demands on a squad that has thrived recently in adversity finally caught up with them.

Klopp said: “We didn’t finish the game off and when you leave the door open away from home at Old Trafford it’s clear they will get chances and they could score the equaliser. Marcus [Rashford] had a big chance at the end of normal time. It was then really hard for us. That was the first time I saw my team really struggling. We played a lot of football recently and then go 3-2 up and all good and then they win 4-3. Come on, you can easily accept that.

“Congratulations to United. They fought extremely hard as well. You want to go to the semi-finals and both teams understood the importance of the occasion and the competition. We tried absolutely everything and didn’t get a lot from it.

“Now the boys have to recover. It’s really tough. They fly all over the world now and in five or six days’ time play the first of two games. Let’s really hope and pray they come back healthy and we can start the rest of the season.”

Coventry v Manchester United
Manchester City v Chelsea

Ties to be played at Wembley on the weekend of 20-21 April.

A brilliant spectacle was marred by tragedy chanting from United ­supporters before and during the match, with Greater Manchester police (GMP) ­making an arrest in ­connection with the taunts. The Football ­Association condemned the ­chanting. A ­significant number of fans in the Stretford End were heard chanting “­Murderers”, “The Sun was right” and “Always the victims” around the hour, with the singing audible to the live television audience.

A police spokesperson said:“GMP can confirm that an arrest has been made in connection with tragedy chanting at the Manchester United V Liverpool fixture this afternoon. Incidents of tragedy chanting will not be tolerated and will be dealt with robustly.” The FA said: “We strongly condemn any offensive, abusive and discriminatory chants in football stadiums, and we are determined to stamp this behaviour out. It is entirely unacceptable and can have a lasting and damaging impact on people and communities within our game. It must stop, and we support any club and their fans who try to eradicate this from the terraces.”