Real were well on top in the opening 45 minutes but could only manage one goal from Karim Benzema, and they were made to pay after the break when Sergio Aguero scored from the penalty spot and Alvaro Arbeloa was shown a red card.
"I think we should have won. We had a lot of chances to score the second goal and if you do that in the first half I think the game should be over," Mourinho said.
"But we didn't score and they had a reaction. They had the penalty that you on TV are in a better position than myself to judge. Arbeloa had a red card and again you have a better position to analyse the situation. After that we have no conditions to win, we played to get the point that gets us to the next stage.
"The only two times I finish second in the group I win the Champions League. I finished second with Porto behind Real and second with Inter Milan behind Barcelona - we win.
"Otherwise I always finish first and I never won the competition. I think it means something because you get a different kind of team, and means you play the second match at home or away, but my experience says it doesn't mean so much."
Mourinho was asked about the events at Chelsea, where Roberto Di Matteo was sacked earlier on Tuesday and replaced by Rafa Benitez.
He added: "That's football. I am never happy when a manager is sacked because it can happen to me and it is a feeling nobody likes to have.
"But at the same time everybody knows I like Chelsea and I always support any Chelsea manager. I wished Roberto well and I do that with the next manager."