Ademola Lookman’s second-half winner condemned the Reds to just their second defeat of the season.
Boss Jurgen Klopp believes his men can forget about catching City if they drop their standards and Van Dijk wants the squad to focus on themselves.
The defender told the club’s official website: “Things can change there. There is no point for us to look at them or look at Chelsea or the teams around us at this point in the season – and we won’t.
“We should look at our performance. We have to improve and take it with us into the next game. We all wanted to do better, that’s a fact and unfortunately, we weren’t good enough.
“I think they deserved the win, but it was obviously down to us. We were poor in the last third, in my opinion.
“It was just overall not a good performance and obviously they didn’t create much, but they looked dangerous on the break, which is what they are obviously good at.
“So credit to them and we have to look at ourselves. Everyone has to look in the mirror and improve and that’s what we will do. That’s part of football as well.”
“This week’s been such a tough week. You’ll struggle to find a harder week in world football, playing Liverpool twice and Man City,” midfielder Kiernan Dewsbury-Hall told the club website.
“It’s just a momentous effort from everybody to regroup, dust ourselves down and go again, basically 48 hours after playing Man City.
“It’s such a rewarding win. Everyone’s so happy and there’s some tired legs in there but that’s what you have to do to beat teams like Liverpool.
“We know what Liverpool are going to bring. They’re a very attacking team and they’re very talented.
“It’s a great save by Kasper to keep it (Salah’s penalty) out and that lifted the crowd and they were great because we need them, especially with quick turnarounds.”