City came from behind to win thanks to an injury-time penalty converted by Erling Haaland.
Van Dijk said at the final whistle: "First half they were much more comfortable on the ball. We tried to be more direct and tried to put the problem in their half but we weren't good enough.
"Second half we were much better and dominant on the ball at times. Dom (Szoboszlai) scored a worldie, they came to press more and got the equaliser. Between the equaliser and the second goal, both teams tried to go for the winner and the penalty moment decides the game.
"You are never in complete control against City, especially when they're 1-0 down, they will press you even more. They play with a sort of 4-4-2 with a diamond in the middle so you have to communicate well. You always have to be on your toes.
"My feeling, maybe I'm wrong, is that we both tried everything to score the winner but a lot of situations and decisions that decided the game as well. Just in general, moments in the game."
On the performance of the match officials Van Dijk also said: "We have no influence on that. Nunes' penalty, he could have given it, he went so fast. We only have ourselves to blame.
"We have to quickly turn our attention to Sunderland because that will be a tough one, unbeaten at home this season. A good challenge ahead."
He added, "It's still a process. The second half maybe felt like a step up but first half we were not in control and should have done better. Unfortunately, the penalty moment was the deciding moment and that is the reality."