City twice looked on course for victory in the second half after being largely on the backfoot before the break.
Edin Dzeko put Roberto Mancini’s men ahead in the 69th minute, before Madrid levelled through Marcelo six minutes later.
But the visitors once again edged in front again when Aleksandar Kolarov’s free-kick flew straight in with just five minutes left.
“No [I don’t have sympathy with Manchester City],” said Mourinho. “That’s football. We deserved to win. If I felt we didn’t I would have more sympathy for them.
“It is a good one because the DNA of my team is back. They [the players] proved to me that if they want to be top professionals and respect Real Madrid’s history they can do it. I’m so happy with the attitude of the players. It is a big victory against a big team.
“This is why people love football around the world. More important than win is to be proud of my team whatever the result.
“I keep saying this to players, when things were not going in the right direction, Real Madrid can lose, they can lose matches, they can lose matches fighting like animals right until the end like they did.”
Meanwhile, City boss Mancini was frustrated by the lapses in concentration that twice allowed Madrid back into the game late in the second half.
“We are disappointed,” said Mancini. “I think in the first half we did not play well but in the second half we did and when you score two goals here and go 2-1 up, you should pay more attention.
“We can’t continue to talk about experience, we have good players playing in their national team and play lot of games. I am happy for our performance in second half and need to improve but we should be disappointed as we lose these points.”
Mancini added: “I think the other teams will lose here. We have five games and it is important we beat Dortmund at home next, will be difficult as they are a top team but this year we want to go through.”