Madrid ran out 3-1 winners at Camp Nou on Saturday but were on the back foot at 1-1 prior to a spot-kick awarded against Clement Lenglet.
Sergio Ramos went down in dramatic fashion following a tug from Lenglet in the area, with the VAR then encouraging referee Juan Martinez Munuera to assess the incident.
He awarded a penalty, which Ramos scored, but Koeman claimed the Madrid captain had first committed a foul.
"Is it a penalty? For me, it is not a penalty," said Koeman, whose side cancelled out Federico Valverde's opener through Ansu Fati but saw any hopes of rescuing a result late on dashed by Luka Modric's goal.
"I hope they can explain it to me about the use of VAR here in Spain. The VAR can be very good, but for all teams.
"I have not spoken with Lenglet about the play. First, it is Ramos foul on Lenglet for taking him by the shirt. Once again, for me, it is not a penalty.
"It is normal for Real Madrid players to do their best so that the referee awards a penalty.
"I don't want to talk about this penalty anymore. What is clear is that it has been decisive in the game."
The victory lifted Madrid above Real Sociedad to the top of LaLiga, while Barcelona sit 12th with two defeats, two wins and a draw from their five league matches under Koeman.