The Italian giants took the lead midway through the first-half when after Dries Mertens raced clear before firing past Alisson.
However, replays suggested that Mertens had deliberately collided with Van Dijk in the build-up to the goal, leaving the centre-back lying on the floor in pain as he charged forward to score.
But following a VAR review, for both the foul and a potential offside, the goal was given, but that didn't stop Van Dijk from making his feelings known on the official afterwards.
"Yeah I'm not going down for no reason," the Liverpool centre-back told beinSPORTS.
“I won the ball and don't think he wanted to challenge for the ball.
“He touched me, I think it is a foul. The referee, I think, didn't have his best day today. That's what it is."
The Dutchman added: "We so far this season never panicked but obviously it is a pity to concede, especially the way we concede as well.
“Think the second half was good. We kept pressing and we kept going at them. I don't think they had an opportunity apart from the goal.
“So yeah, we are disappointed we didn't win."