Goals from Juan Bernat and Neymar proved to be enough for PSG at the Parc des Princes, despite a penalty from James Milner on the stroke of half-time.
The Reds now must beat Napoli 1-0, or by two clear goals should the Serie A side score, in their final Champions League group game on December 11.
The Reds are swiftly back in action however, with Sunday afternoon's encounter with Everton at Anfield highly anticipated.
And van Dijk has his sights set on the Merseyside derby, a game in which he scored the winner on his Reds debut in the FA Cup third round in January.
"It’s always a fantastic game to play in and obviously for me as well it was my first game for the Reds," he added.
"Hopefully we’re going to make it a special one again. We need to win, that’s the only thing.
"If I can contribute with a goal then it will be fantastic. It’s always good to look forward to such a game."
The derby between the two fierce rivals will undoubtedly be highly charged and full of strong tackles, and it remains to be seen how the Reds respond after a similar encounter in Paris.
The Netherlands international added he was frustrated by the home side's antics, however admits the Reds may need to do the same when needed.
“Obviously they’re world-class players but I don’t think it’s needed in the game at times,” he added.
“Sometimes they get hit and they will go down and sometimes I think it’s too easy and I’m getting so frustrated. It’s important to keep your head cool but...
“Every time we made a foul they all came to the ref trying to get us a yellow card. We should do the same at times and I think in the second half we did it better. It’s not the type of game that I like.
“We still respect them and how they are as players because they’re world-class but it’s not really necessary at times. But they scored two goals, we lost and that’s it.”