Van der Vaart made the remark during his half-time analysis for Dutch broadcaster NOS at the Netherlands' opening 2-2 draw with Japan in Dallas, saying he was "quite shocked" by the 34-year-old centre-back's first-half performance.
"With him, I thought: that doesn't look good. Especially while turning. It is proving very difficult. A bit like a Boeing 747 turning. I hope he starts turning a bit faster during the tournament."
Klopp, who signed Van Dijk from Southampton for £75 million in 2018 and managed him for six years on Merseyside, was working as a pundit on German television when the Netherlands beat Sweden 5-1 in Houston the following weekend. He used his platform to defend his former captain without sentiment.
"I don't know if it's worth naming Rafael van der Vaart at all. But if he ever says something positive about a player, I'm willing to take him seriously again. You have the feeling that he sees something, which then has to be expressed in a flowery way and then he goes against it."
Since then, Van der Vaart has revised his assessment in his column for AceOdds.com.
"Van Dijk is still our leader. And I think he is performing well. He was one time turning a bit slow against Japan, but this is normal. He had a bad injury and a tough season at Liverpool. He is not getting younger, and for me it looks like he always tries to get the team to stay compact because that benefits him as a player."
He pushed back against the broader narrative building around the Dutch captain.
"However, if we truly analyse him honestly, he is still one of the very, very best. Look at how easily Saibari outran Gabriel, who is considered in England the best centre-back. I was watching Saliba in the France game, and I saw quite a few mistakes. Compare Van Dijk with other centre-backs, and it's clear that even at a so-so season, he is still elite. He is still our best defender. Without a doubt."
Van der Vaart was careful to place the criticism in a cultural context.
"He has been unfairly criticised by some in the Netherlands, but he is still our captain and our leader. But our nature is to criticise. One day you are the king, the next day you are s***."
Van Dijk played in Holland's 5-1 group stage win over Sweden in Houston. The Netherlands have qualified for the knockout rounds with maximum points from two games.