The Reds got their title defence up and running with a victory at Anfield on Saturday, but it was far from straightforward for Jurgen Klopp’s side.
Newly-promoted Leeds equalised three times during an extraordinary match, only for Mohamed Salah’s late penalty to earn the home side the victory.
Van Dijk was guilty of making an uncharacteristic error for Leeds’ second goal and Liverpool legend Carragher slammed the Dutchman over his ‘arrogant’ defending.
‘That’s just too arrogant,’ Carragher said while commentating on the match for Sky Sports.
‘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.’
Addressing the mistake in an interview with beIN SPORTS, Van Dijk said: ‘It was one of those… they are situations that can happen.
‘I always try to do my best and that’s what I did. Unfortunately a goal came from it but I don’t worry about that.’
On Liverpool’s hard-fought victory, the Netherlands defender added: ‘We expected an intense match.
‘No one wants to concede goals but it was intense for both teams. We trained for that and we knew that could happen.
‘The points are massive of course. They [Leeds] will trouble many teams in the league I think so it was good for us to get the three points.
‘But we still have things to work on.’
Van Dijk also hit out at those still doubting the class of Liverpool team-mate Salah, who bagged his third Premier League hat-trick in the 4-3 win.
‘That’s the media, that’s you guys who were doubting him,’ Van Dijk said. ‘We appreciate him and that’s the most important thing for him.’
Liverpool, who won the Premier League by 18 points last season, face Frank Lampard’s Chelsea next weekend.