The 26-year-old defender played the full 90 minutes at St Mary’s as he featured against his former club for the first time since his January transfer to Anfield from Southampton back at the start of January.
Van Dijk has been a regular fixture in the first team at Anfield since his £75m transfer to Liverpool FC from Southampton.
The Netherlands defender produced a solid performance on Sunday as he helped his side to keep a clean sheet and seal a 2-0 victory thanks to goals from Mohamed Salah and Roberto Firmino.
And Liverpool FC boss Klopp has admitted that he was thrilled by the attitude shown by the defender in Sunday’s game.
Speaking at his post-match news conference at St Mary’s, Klopp said: “He did really well, he dealt with the situation fantastically.
“We had a little talk before the game and I asked, ‘What do you think?’ He said, ‘No, I’m fine boss’.
“I don’t want to make him nervous if he isn’t nervous and obviously he wasn’t and that’s good.
“I understand everything in football; the crowd is there to make life difficult for the opponent but I think it was not too difficult for him from this point of view and I’m happy about it.”
Van Dijk will be hoping to feature for Liverpool FC when the Reds take on FC Porto in the last 16 of the Champions League on Wednesday night.
The Reds are aiming to progress through to the quarter-finals of Europe’s elite club competition as they also bid to try and finish in the top four in the Premier League.
Liverpool FC are yet to win their first trophy since Klopp’s appointment at Anfield back in October 2015.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news