Van Dijk appeared to foul an opposition player late in Liverpool’s 1-0 win away to Crystal Palace.
He tussled with England star Marc Guehi in the box, but no foul was given and VAR did not overturn.
“The referee’s call of no penalty for the challenge by van Dijk on Guehi is checked and confirmed by VAR - deeming that the challenge was not sustained holding and had no impact on the play,” the statement said.
Speaking post-game, Van Dijk told TNT Sports: "It is hard to come here. The results over the years are tight and close.
"I think obviously we scored a fantastic goal. We could have done better in the second half, but we knew they'd come out with a bit of pressure on the ball. It ends our run on a high before the internationals.
"We keep going and we keep working. We are never satisfied. We needed Alli (Alisson) twice, but that is what we try to avoid. Everyone is contributing to clean sheets.
"I think there is always expectations towards different teams - whatever the outside world thinks of us we don't really care. We want to try to challenge, compete, win and be successful."