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 which spanned the half-time break, scoring twice either side of the interval following 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 for 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.”