The Reds won 3-0 via first-half goals from Luis Diaz (2) and Darwin Nunez.
Van Dijk said afterwards: "Obviously coming off a good performance in Milan, it was important to keep going, don’t be satisfied and obviously in the first half three good goals. We could have scored more, in my opinion, maybe should have. But Bournemouth are still a very good team and they created some difficult moments and we had to fight. Overall, very happy with the clean sheet, 3-0 and now we focus on the Carabao Cup.
"I think a game is 95 minutes, something like that, or maybe 100 minutes in total. So there is plenty of time to come back from it if you have a setback. Obviously it was offside so we just kept playing and kept trying to do the same things that the plan was before the game. It was a good first half in terms of the goals we scored, I think we maybe could have controlled the game a little bit better. But we are satisfied, we take the three points, 3-0, a clean sheet and we move."
On bouncing back from the Nottingham Forest defeat, he continued: "We spoke about it the day after a lot and obviously in the build-up towards Milan. But after that, life goes on, we had another chance to win a game and that was the case obviously in the Champions League. And today was another opportunity and we grabbed it, so now we focus on the next one.
On Nunez scoring in his first start of the season, Van Dijk added: "Obviously happy for him. He has to keep working, keep being important when he has the chance. Obviously he has a very good ‘opponent’ or ‘rival’ or however you want to call it in Diogo Jota with him, so they have to challenge each other and push each other. That’s the only way we can be successful. The way he responded today after his first start of the season is obviously the one we want to see. He has to keep working, like the rest of the team."