After seeing his team beaten 3-1 at Camp Nou last month, the Dutchman hit out at the decision to award Sergio Ramos a penalty just past the hour mark.
He also claimed that Barca had been the victim of a number of incorrect calls in other games so far this season.
An incensed Koeman said: "I don't understand the referee's decision, only VAR appears when decisions have to be made against Barcelona.
"Decisions are always against us. He tells me it's a penalty, it's incomprehensible. I didn't like it.
"I told the referee that I hope they can explain to me one day how VAR works in Spain, because we have played five games and VAR has always been against Barcelona.
"However, it did not intervene in a penalty play on Messi against Sevilla or two red cards against Getafe. Why is VAR always against us?"
As a result of those comments, the RFEF have now opened disciplinary proceedings that could result in a ban last anywhere between two and 12 games and a fine of up to €3,000.
Barcelona director Xavi Vilajoana is also in hot water with the Spanish football authorities for posts made on Twitter in the aftermath of the Clasico.