Real had defender Raul Albiol sent off on 53 minutes for conceding a penalty and trailed 1-0 after Lionel Messi converted the spot-kick, but Cristiano Ronaldo's 82nd-minute penalty levelled the match.
Madrid trail Barcelona by eight points in the league and Mourinho said he was fed up with what he sees as a lack of consistency from referees.
"I am tired of playing with 10 men against Barcelona," said Mourinho. "One day I hope to play with 11 men and our rivals with 10.
"We played very well with 10 players. We played with a lot of dignity and character and with the fans absolutely fantastic, and we almost won.
"In my opinion it was a very even game when it was 11 against 11. In the first half the teams respected each other, knowing they were facing strong opponents.
"It would be mission impossible for many teams, especially against a side who are the best in the world at keeping possession.
"But once again we've been left with 10 men, a lot of time with 10 men, and once again there's been an absolutely incredible difference of criteria."
Mourinho was furious that Barca's Brazilian right-back Alves was not sent off for bringing down compatriot Marcelo to concede the penalty that Ronaldo converted.
"I don't understand the reason why Dani Alves hasn't seen a second yellow after conceding a foul in the area for a penalty," said Mourinho.
"I asked the fourth official why there wasn't a second yellow and he told me: 'It's because he's a full-back.'
"When everyone thought they could destroy us playing with one player more, for 45 minutes the team was strong enough to compete and strong enough to get a result, and if the referee gives, as he should have done, a second yellow card to Alves, the last 10 minutes playing 10 against 10, it could have been a different story."
Real take on Barcelona again on Wednesday in the King's Cup final at the Mestalla stadium, with Mourinho aiming to win his first trophy with Madrid.
"The cup final is unique and one team will go home with the cup and the other with nothing," said the Portuguese.
"We will try to win the game and don't need to study Barcelona too much because we know each other perfectly well."
Barcelona and Real will also face off twice in the Champions League semi-finals, with the first leg at the Bernabeu on April 27 and the return leg on May 3 at Camp Nou.