The top-of-the-table clash was billed as a key fixture in the context of a title race of which Liverpool are now firmly in charge.
Star centre-back Van Dijk, who was at pains to highlight the gruelling schedule that lies ahead of the Reds, acknowledged the match carried extra meaning.
"It's like any other three points, of course, but it was a bit special because you are playing against the champions, your direct rival, and I think it was a very good game to watch," the Netherlands international told reporters.
"Obviously we are very happy to get the three points.
"We all know and we all feel there are so many games left that so many things can happen between now and May.
"The only thing which can happen is for everyone to stay fit and we need everyone to play as well as they can. We are very happy with the position we are in, but we cannot take it for granted. We just have to keep going and take it game by game.
"You can imagine everyone is happy we got three points again, especially before an international break.
"It is not a nice feeling if you go into the international break having dropped points, especially at home, so we were very good, and we had to be if we were going to get the three points."
City roared back from a seven-point deficit at the turn of the year to beat Liverpool to the title last term and Van Dijk expects Pep Guardiola's side to mount another strong challenge.
"They are the champions first of all, so they will definitely be up there again," he said.
"The other teams have been doing well. The only thing we focus on is the game ahead of us, it's pretty boring that I keep saying it, but it is actually a fact. Let's just go for it."