Ferran Torres had briefly given Barca hope, making it 2-1 in the 83rd minute, but a late penalty awarded for Eric Garcia's foul on Rodrygo allowed the Brazilian to seal the three points from the spot.
Barca were angered that the penalty decision was made after the referee was advised to check the pitchside monitor. The referee did not review an earlier penalty claim for a Dani Carvajal challenge on Robert Lewandowski at the other end.
"Once the game had ended and with the refereeing team back in the dressing room, Barca president Laporta came in repeatedly asking for an explanation on certain decisions made in the game," the referee report said.
"Laporta was asked to abandon the dressing room without any further incidents occurring."
Barca coach Xavi Hernandez recently called for referees to give news conferences after games following what he perceived to be decisions that went against his team in the recent Champions League loss to Inter Milan.
However, Xavi did not comment on the refereeing at the Bernabeu, as Barca lost for the first time in LaLiga this season to see their seven-game win streak end.
"Sometimes you find yourselves on a bad run, but luckily it's just three points," Xavi said in a news conference. "We tried, we showed faith. It was a good chance to stay top of LaLiga, it just was not to be.
"We did not take advantage of the moments when we were on top. Madrid defended well, and the feeling is we're on a bad run and nothing is coming off. Like I say, it's just three points and the season is long, although that is not much of a consolation right now."
Xavi, who referred to his Barca side as a team "in construction" following over €150 million of investment in the summer, said the difference between his team and Madrid boils down to maturity.
"I would not say they were more intense; I think it comes down to maturity, knowing how to compete," he said.
"The sensation I have is that we competed worse than Madrid. That's why they won, because they compete well and they know what they have to do. They are a more mature team than us at the moment.
"We spoke about the situation for the first goal, for example, and it cannot happen. We have to make the foul. Madrid took advantage of the three counter attacks they had.
"I am worried that we are not attacking well. We are not taking advantage when we are on top. It's not been a great day. We're on a bad run, and it has to change now. We have to be more mature and compete much better."
By the time they face Bayern, they could already know their fate in Europe. If Inter beat Viktoria Plzen earlier on the same day, Barca will be eliminated from the group stage for the second season running.