Real were furious that Atletico defender Cristian Romero was not sent off for a stamp on Jude Bellingham and also complained about a challenge by Lee Kang-in on Federico Valverde, before the visitors were themselves reduced to 10 men five minutes after halftime.
"We could skip the press conference because the story of the match is right here," Mourinho said, holding up the images in what was the start of a near five-minute rant.
"Those were two clear red cards. The difficulties we've faced since the sending-off. 11 against 10. Well, we can imagine what 50 minutes of 11 against 9 would have been like if justice had been done."
Real defender Dean Huijsen was dismissed for bringing down Giuliano Simeone inside the area as the last defender, allowing Alejandro Grimaldo to score with a low spot kick. Jonathan David doubled Atletico's lead six minutes later, with Antonio Rudiger heading in a free kick late to reduce the deficit.
Mourinho said he could only "hug" his players after what he described as a first half "full of class and great character", but he aimed sharp criticism at referee Miguel Angel Ortiz Arias and those who appointed him.
"They've put a referee, aged 41, with no international experience – it's certainly not because he's a great referee," Mourinho said.
"Then the poor chap has come here and hasn't been able to cope with the pressure – and it really is intense pressure. I call it '80s-style pressure' here in this stadium, which you hardly ever see these days."
Asked about being six points behind Barcelona, Mourinho offered a pointed reply.
"If they just leave us in peace and let us compete on a level playing field with everyone else, we've still got a long way to go," he said.
"I don't want to go so far as to say this was set up... I want to believe that they simply made a mistake."
Asked about Mourinho's comments, Atletico manager Diego Simeone urged restraint.
"Whoever is speaking – be it me, Mourinho, Hansi Flick or Manuel Pellegrini, anyone – we have to be careful what we say," Simeone said. "When you step outside the bounds of respect, whoever you are, it's not on. You can't cross that line."
Simeone preferred to focus on Atletico's performance.
"Today we saw a great match; we defended very well against a team that plays very well," he said.
"We controlled the match when it was 11 against 11. We continued to control it when it became 10 against 11. But this isn't just another step towards continuing to grow and improve."
Atletico climbed above Real into second in the standings on 16 points, five behind leaders Barcelona and one ahead of Real and Real Betis.
