Van der Vaart took issue with Van Dijk refusing to declare themselves champions-elect after the 2-0 win.
"We will not do that, we will not be like that," Van Dijk told Ziggo Sport. "We know like no other, since last year, that things can go crazy. We lost one game last year and you still do not win the Premier League. We just have the mentality that we want to go match by match right now. Even after today we can do even better, at times.
"We focus on that, we don't want to look any further. We are not going to walk beside our shoes."
In response, Van der Vaart declared: "When does it become unbelievable? I think it is already quite unbelievable.
"I don't think it's strange if you're up by sixteen, and probably nineteen, points, then you say, 'I think we're going to be champions'. Is that crazy?
"Instead you'd better say, 'Listen, if we give this away, we'll never get over it'. That's just how it is.
"They are not going to blow it now, but you notice that there is something about it throughout the club: take it easy, because..."