Liverpool captain Virgil van Dijk has apologised to the club's supporters and said his side "gave up" as they were dumped out of the FA Cup by Manchester City.

The Reds' hopes of winning silverware this season now rest on Champions League glory following Saturday's humbling 4-0 quarter-final defeat at Etihad Stadium.

Manchester City demolished Liverpool in an 18-minute period spanning the half-time break, scoring twice either side of the interval after an evenly matched opening half an hour.

"I can only apologise to the fans for what we have shown, especially the second half," said Netherlands centre-back Van Dijk, 34.

"Obviously, you come out with the right intentions from the dressing room [after half-time], to hopefully score 2-1 as soon as possible to change the game.

"The opposite happens, and to come back from 3-0 is obviously very difficult here, but also you shouldn't give up, and that's maybe, at a certain point, what happened.

"We let our fans down, we let ourselves down, and the manager.

"The way we played in the second half, especially, must hurt for everyone. It definitely hurts me."

'Everyone has to look at themselves'

It was Van Dijk's foul on Nico O'Reilly which gave Erling Haaland the opportunity to kickstart City's demolition job from the penalty spot after 39 minutes.

The Norway striker went on to complete a hat-trick in the second half with 57 minutes played, after Antoine Semenyo had added his side's third.

The result and performance increases the pressure on manager Arne Slot, who led the club to the Premier League title in his first season in charge last year, before the first leg of their crucial Champions League quarter-final tie against Paris St-Germain.

On his manager, Van Dijk said: "It's a together thing, isn't it? Obviously, he's responsible as the manager, but we are the ones on the pitch who have to do it.

"The matter of fact is now, PSG are waiting for us. I watched them a little bit on Friday. It will be so tough again. So we have to be ready mentally as soon as possible."

Liverpool travel to Paris for the first PSG game on Wednesday (20:00 BST), before hosting the French champions the following Tuesday.

Fifth in the Premier League, they host Fulham between those European matches in another key fixture in their bid to qualify for next season's Champions League.

"If we want to make something out of this season, then we have to try and produce something special in the next three games," Van Dijk said.

"I'm trying to think how we can turn this around. We've been going through this for almost 75% of the season.

"We fall back into games where we get beaten on intensity or how much you really want to go for it. It's a difficult one to take, and everyone has to look at themselves."