Writing in today's match programme notes for their clash with Bournemouth, Van Dijk says their opening Champions League win was the right reaction to the Forest setback.
He wrote: "We know that we fell way short of the required standard against Forest, and that hurts.
"We don't lose many games at Anfield, so it was inevitable that people were wondering how we would react as we headed to Milan. And apart from the first five minutes, I think we answered the questions.
"It was a difficult start, but the way we worked after going behind was outstanding. It would be easy to lose composure going 1-0 down so early in the game, against a good team in an iconic stadium, but we stayed calm and kept looking for the solution, which was very good to see.
"From a personal perspective, it was good to get my first goal of the season, and it was good to see Ibou Konate get his first for a good while too. We may be defenders first and foremost, but we both know the importance of chipping in at the other end as well, and for us both to get on the scoresheet was very pleasing.
"Any away victory in the Champions League is hard-earned, especially against a team like Milan, so we were very happy with the way we controlled the game thereafter, and it was great to see our travelling fans celebrating at the end.
"We know that you guys have been as desperate as we have to get back into the Champions League, so this was a pretty good way to return."