The recently arrived manager has the unenviable task of replacing Jurgen Klopp.
While Slot has seen his side start the season impressively, Van Dijk knows only one or two poor results can lead to the knives sharpening.
Days after they lost 1-0 at home to Nottingham Forest, Liverpool captain Van Dijk said: “In football you have to deliver today and tomorrow and if you don't then the pressure can pile up from the outside but we have to stay calm.
“Obviously I have a big role in that, the manager has a big role in that and we as players have to show it on the pitch. We have to - and I said it after the game - we have to stay calm and focus on our targets but going back to that game, losing at home to Forest, no disrespect to them, just us losing at home is a reality check and a shock.
“It can't happen if you want to achieve things that I want to with the club. So Milan was a good reaction and now it is recovery, go home and Saturday is a big one.”