Five goals were scored during a remarkable first 45 minutes at Anfield on Saturday evening, with defending champions Liverpool leading newly-promoted Leeds 3-2 at the break.
Mohamed Salah gave the Reds the lead on four minutes with a penalty, but Leeds were level shortly through Jack Harrison.
Van Dijk then headed Liverpool in front from Andy Robertson’s corner, before a sloppy piece of defending from the Dutchman saw Leeds equalise for the second time.
Attempting to deal with Harrison’s lofted through ball, Van Dijk swung a leg but failed to connect with any real conviction, presenting Patrick Bamford with the chance to score.
The Leeds striker made no mistake, slotting the ball past Brazilian goalkeeper Alisson.
Commentating on the game for Sky Sports, Liverpool legend Carragher said: ‘Virgil van Dijk, that’s just too arrogant.
‘He tries to flick it around rather than just dealing with it. Maybe that’s because it’s Leeds United, a new team, and he thinks it’s a little bit too easy.
‘But Patrick Bamford has been given a gift by that man.’
Three minutes after Van Dijk’s error and Bamford’s goal, Salah smashed in his second and Liverpool’s third of the evening off the crossbar.
Former Leeds and Chelsea striker Jimmy Floyd Hasselbaink added: ‘Leeds worked it really well but he should handle this. Van Dijk doesn’t look great.
‘It’s just a normal ball he should clear, he tries to be smart but it doesn’t work and Bamford scores.’
Liverpool legend Graeme Souness, meanwhile, said: ‘He [Van Dijk] has had an absolute stinker.’
Jurgen Klopp’s Liverpool are bidding to defend their Premier League title, having finished 18 points ahead of second-placed Manchester City last term.