Koeman saw his side’s chances of winning the Spanish title take a major hit at the home of their rivals, though they remain just a point behind the league leaders.
Atletico Madrid are a point ahead and have a vital game in hand following Barca’s defeat against Zinedine Zidane’s side.
Koeman was interviewed after the game, but stormed off after a question about a penalty shout.
The Dutch boss felt Barca should have been handed a penalty after Martin Braiwthwaite went down inside the box.
Despite it appearing that Ferland Mendy had pulled the Danish striker to the ground, the referee was having none of it.
And Koeman was left enraged by the decision, as he stormed out of an interview after discussing the penalty incident.
He said: “In the 1st half we weren’t good. In the 2nd we improved.
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“I just ask refs to accept decisions.
“It was a penalty… It was really clear.
“But we have to accept it and shut up.
“It was really clear. Really clear. (to interviewer) You saw it, was it a penalty?”
After the interviewer didn’t respond, Koeman walked off.
Oscar Mingueza’s goal after the hour wasn’t enough to turn around the scoring after Karim Benzema and Toni Kroos’ first-half efforts.