Koeman's side were edged 2-1 by World Cup champions France last month, Van Dijk beaten to a cross by Olivier Giroud for the winning goal in the Nations League clash.
Van Dijk, widely regarded as one of Europe's best defenders, also gave away a penalty for Liverpool against Manchester City on Sunday, but Riyad Mahrez sent his spot-kick over the bar.
Koeman, who signed Van Dijk at Southampton in 2015, said he wanted more from the star centre-back.
"I told Virgil within 30 seconds of the end of the game against France what I thought," he said.
"I know him so well – and that means I know where all his little faults are.
"Virgil has to improve, not a lot, but sometimes he is a little too laid back. That needs to change.
"There are moments as a defender when you should be no more than three feet away from the striker you are marking.
"And, particularly in Van Dijk's case, because of the strength and power he has he is too laid back."
For his part, Van Dijk insisted that his manager had every right to be critical of his recent mistakes.
"He's not strict. He's well within his right [to say that]," said Van Dijk. "He has every right to be critical. He wants to make us better."