The Reds' Champions League defence got off to a disappointing start at the San Paolo thanks to late goals from Dries Mertens and Fernando Llorente.
Mertens' opener came from a contentious penalty before Llorente capitalised on a slack piece of play from Van Dijk to seal the win and put pressure on Liverpool ahead of Wednesday's meeting with Salzburg at Anfield.
Klopp says his faith in the Netherlands star has not at all been shaken by that incident, and he is not ready to panic about their chances of progressing to the knockout phase after only one match.
"Yep, I think so. I'm really happy with all my other defenders but yeah, he is the best at the moment," Klopp said on Tuesday when asked if he felt Van Dijk was the best in the world.
"We conceded in Napoli… which country are you from? Italy? I thought so… I still think it was not a penalty!
"Napoli have to come to Liverpool, so it's not decided yet, but we lost the game, that's a fact as well and we have to start winning.
"We don't even have a little bit of a feeling that this game tomorrow is half done. It's not. They will surprise a lot of people. But if there is anybody in the world who knows most about how they do what they do, it's me.
"I have a pretty good side as well and we want to be the most uncomfortable opponent in world football and if we are that tomorrow it's not easy for Salzburg."
Salzburg thrashed Genk 6-2 on matchday one, with 19-year-old striker Erling Braut Haaland scoring a hat-trick in that victory.
Klopp says he has a plan to deal with the rising Norway star, who has hit 11 goals in seven league starts this season.
"Norway has good footballers!" he said. "A wonderful player, very young, confident, looks focused. A proper player and in a decent place at the moment. He's not the only threat for Salzburg, unfortunately, but he is a proper one.
"Yes [we have a plan to stop him], and you have to watch the game tomorrow to see it."