Liverpool boss Jurgen Klopp said he took encouragement from an improved performance as the FA Cup holders crashed out of the tournament after suffering a late 2-1 defeat to Brighton & Hove Albion in the fourth round on Sunday.

Harvey Elliott opened the scoring on 30 minutes at the Amex Stadium, but the hosts hit back through a deflected Tariq Lamptey strike on 39 minutes that was credited to defender Lewis Dunk, before Brighton claimed a narrow victory thanks to a stoppage-time winner from Kaoru Mitoma.

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The defeat meant Liverpool's FA Cup title defence came to an abrupt halt and have won just three in nine games since the World Cup break -- the worst of which came in a dismal 3-0 defeat to Brighton just over two weeks ago. However, Klopp said his side's performance was improved from their recent visit.

"We came here after a couple of weeks with one of the worst performances in my time here, so today it was much better, but still we conceded two goals from set pieces," Klopp told reporters after the match.

"So now we closed the gaps where they passed through last time, but they scored from set pieces.

"We still have space for improvement. We make steps but we have to improve, we have to go further on and we will do that."

Having been knocked out of the Carabao Cup in December and trailing Premier League leaders Arsenal by 21 points, Liverpool's final hopes of winning silverware this season will come in the Champions League, where they face holders Real Madrid in the round of 16.

Klopp said Liverpool could have been better in Sunday's FA Cup exit and called for his team to get back to the form that saw them lift both domestic trophies last season.

"I think this is a way you can get knocked out of a cup competition," he said. "In a better situation -- say 10 points ahead in the league -- and you lose to Brighton, you have to respect what they do.

"We work now to make that final step, that's why it feels especially bad in this moment because it didn't happen. But again, there were steps in the right direction.

"We have to build on these games, we have to improve and to do better. The body language on a couple of the boys has to be better, defending in formation must better.

"I think last game here we couldn't have won. We were lucky they didn't get more. But this today nobody would have been surprised if we won this game, so that is good. But today we were not good enough which is why we are out."

Liverpool return to action against Wolves in the Premier League on Feb. 4 before taking on rivals Everton in the Merseyside Derby on Feb. 13.