Van Dijk and the former Manchester United captain have traded barbs in the press over the Dutchman's form over the past week.
Following the victory at Anfield, Van Dijk spoke with a panel which included Rooney.
He said, "Of course, if you lose four or five games in a row as a Liverpool player then it is a fair criticism, that is absolutely normal in that sense. But I think it is over the top at times as well at that point, but that is because we live in a world with so many platforms and so many people can say stuff, it will be picked up and made bigger.
"I think it is good that ex-players who played at the highest level who dealt with difficult moments as well puts a lot in perspective (said with a smile as Rooney laughs)."
Rooney then said: "I am not saying anything any more because I think I spurred them on and put them on a winning streak!
"I think what I've said was fair when you win the Premier League and then go on a run where you lose three or four games in a row, which you don't expect from Liverpool over the last few years.
"As Virgil is captain I think that is your opportunity to go and lead the players and that is what I was saying. That happens in football and I think the response has been great from Virgil and the team."
Van Dijk said before embracing Rooney: "I think if you watched games then I would definitely take responsibility. I think the comment that I signed my new deal and then it was like 'that is it' and I let it slide, I think that was a bit... but that's my personal opinion and we move on."