MANCHESTER, England, March 17 (Reuters) - Manchester United's ( MANU ) stunning 4-3 comeback victory over Liverpool in extra time in the FA Cup quarter-finals on Sunday kept their trophy dreams alive and manager Erik ten Hag hopes it will also be the catalyst to turn around their Premier League fortunes.

Amad Diallo practically blew the roof off Old Trafford when he netted the winner in the 121st minute after Marcus Rashford equalised eight minutes earlier and the 12-times FA Cup winners booked a semi-final spot against second-tier Coventry City.

"This could be that (pivotal) moment where the team can really believe, and the energy too, that they can do amazing things," delighted Dutchman Ten Hag said.

"And I think when you can beat Liverpool in the way we did, that you can beat any opponent, so it's up to us to prove the point. I said this also on Friday (in the pre-game press conference) -- and today we did."

United are sixth in the standings, a massive 17 points behind Liverpool in second but, more importantly, they are nine points off fourth-placed Aston Villa in the race for a Champions League spot for next season, albeit with a game in hand.

Former United captain Roy Keane suggested Sunday's thriller could galvanise the team, particularly the youngsters.

"A lot of players have never had Old Trafford bouncing like that. The feel-good factor for these players can be massive for the rest of the season," Keane said on ITV.

United has indeed been a dreary place on many nights this season, but Sunday's battle will go down as a classic.

"When it's Manchester Untied against Liverpool, it's one of the world's best football matches. It is historical," Ten Hag said. "I thought the first 35 minutes were the best I have seen from my team this season."

United's rivals and FA Cup holders Manchester City face Chelsea in the other semi-final at Wembley next month.