The Reds won 2-0 via goals from Luis Diaz and Mohamed Salah on Sunday.
Van Dijk said, "I think it was good game. We didn't concede many chances, scored good goals and so many good things. Maybe a couple of things we have to improve and lots of things we can build on.
"I think at times we could have been a little more patient and let them run from side to side a bit more. I think if we stayed more calm we could have more space at times but it is still a work in progress. It's a good time and hopefully we have so much to improve and go for it."
On working with Arne Slot, he continued: "I was excited. The responsibility I have on the pitch has always been there but in possession and the way we play, centre-backs are important to the way the manager wants to play."
On playing 100 games at Anfield with just two losses, the Dutchman smiled: "That's not bad and I am really proud of it. I am still gutted about the two losses! I am proud of that. It is home and home should feel very comfortable. Credit to the fans and the team. Let's make it an amazing season and then we will see."