Erling Haaland broke the deadlock just three minutes after Gravenberch’s dismissal before Jeremy Doku doubled Man City’s lead with a brilliant curling strike.
Rayan Cherki added a third on 78 minutes as Manchester City’s first game since being found guilty of ‘serious breaches’ of financial rules ended in an emphatic victory.
Asked about Man City’s guilty verdict after Liverpool’s deflating defeat, Van Dijk said: ‘The only thing I can say, because it’s ongoing, is that I have really enjoyed the rivalry.
‘But that is on the pitch, what has happened off the pitch is a totally different story. Because it’s still ongoing, it’s not a good idea for me to comment on this.
Man City thumped Liverpool at Anfield (Picture: Getty)
‘When it’s properly settled I will definitely share my comments on it but for now let’s wait and see.’
On the game as a whole, Van Dijk added: ‘First half was good from us. We showed our intensity, could’ve done better on occasions where we got on the break.
‘They weren’t massive chances but we showed we wanted to win and we had intensity which is the bare minimum.
Liverpool midfielder Ryan Gravenberch was sent off (Picture: Getty)
‘Second half the red card changed the game, especially when you concede quickly afterwards. We end up with 10 men is the fact and we concede quickly after and it becomes a difficult game against them again.
‘I think the atmosphere is always good here, I’ve been fortunate to play in a lot of big games here.
‘For other players maybe it was different but for me I was ready to compete and I think we showed that especially in the first half.’
Jamie Carragher believes that “there’s no way Man City can be allowed to win the league if they’re found guilty” 💬 pic.twitter.com/y7iWowsn8d
Liverpool boss Andoni Iraola, meanwhile, said he was ‘very proud’ of his players despite a disappointing defeat at home.
‘I think the first part is that we played two different games,’ he said. ‘One until the red card, and then after.
‘For 60 minutes, the players were very good. The second game from the red card was where City were better than us.
‘The first yellow card was just a kick in the toe. It was nothing. It was a normal foul. It was the moment when we were pushing more.
‘The momentum was coming for us and the atmosphere in the stadium was so nice. We conceded very little in the first half. We did a really good job. The second half, we were translating into chances.
‘You learn a lot in games like today. I am very proud of my players. They put the work rate and everything in today. It’s a loss and we didn’t get anything from the performance but I liked it a lot.’
Man City’s win sends them three points above defending champions Arsenal, while Liverpool slip to ninth with just two wins from six.
