The defeat has heightened pressure on Arne Slot as Liverpool enter a pivotal stage of the season.
Dominik Szoboszlai had earlier put the hosts ahead with a superb free-kick, but his influence was curtailed when he was sent off after a VAR check, leaving Liverpool vulnerable late on.
City took advantage, with Bernardo Silva equalising before Erling Haaland – largely contained for much of the contest – converted a penalty to seal the turnaround. A dramatic late moment saw Rayan Cherki’s third goal ruled out by VAR, offering scant consolation.
The defeat highlighted familiar defensive issues for Liverpool, who have now conceded six stoppage-time goals this season, costing them eight points.
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“I think you can’t compare all of the goals [conceded in stoppage time],” Van Dijk said.
“I think maybe you can compare the Crystal Palace goal and the Bournemouth goal but this one you can’t compare with the others. But the fact is that we conceded that late on and I keep saying it but we have to do better in this.
“You also have to remember that you’re playing against City, who are obviously very comfortable on the ball, and at times, when you don’t win the ball, because we did many times as well, I think making the right decisions could have been better.
“But yeah, it’s easy now to maybe say that we dropped off too much and that’s why they scored the equaliser. Overall the feeling that I have right now is that in the first half we weren’t good enough, in the second half we were much better but still disappointed we lost.
“At the moment [we don’t take positives] because I’m disappointed that we lost. But I will do everything in my power to recover and then we’ll discuss it and then we have to turn our attention very, very quickly to an opponent that is having a very good season, especially at home, so it will be a big battle.”
The loss comes amid an ongoing injury crisis, further complicating Slot’s task as Liverpool chase Champions League qualification with 13 matches remaining.
Attention now shifts to Wednesday’s trip to the Stadium of Light to face Sunderland, who remain unbeaten at home in the Premier League this season.