Roberto Mancini's side required a win to keep their hopes of progression alive, but could only draw 1-1, with Sergio Aguero's late penalty cancelling out Karim Benzema's 10th-minute effort.
The Italian claimed after the game that the club's Arab owners had not expected to get through the group stage, but the Portuguese boss believes they should have challenged.
"With the players City have, it's incredible they haven't qualified two years in a row," Mourinho told reporters.
"If I had been knocked out of the Champions League in the groups, I wouldn't have been able to go back to Madrid."
Mourinho reflected on Madrid's 1-1 draw against the English champions and was disappointed not to have come away from the match with more than a point, despite a dominant performance.
"I think [we deserved to win] because we had plenty of chances to score the second goal, and if you do that in the first half, the match should be over early on," he continued.
"But we didn't score. [Man City] reacted and got the penalty that you on television are in a better position to judge.
"Arbeloa was shown a red card. Again, you are on TV and in a better position to analyse the situation. After that, we were in no position to win and we played for the point to progress to the next round."
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The 49-year-old's previous club Chelsea sacked Champions League-winning coach Roberto Di Matteo earlier in the day, but while he sympathises with the Italian, he will offer his unrequited backing to former rival Rafa Benitez.
"That's football," he admitted. "I'm never happy when a manager is sacked because it can happen to me and it's a feeling that nobody wants to have.
"At the same time, everybody knows I like Chelsea and I'll support any Chelsea manager, the same way I supported Roberto and I wished him to do well. I'll do the same for the next manager."
Los Blancos had to beat Manchester City on Wednesday to have any chance of progressing to the knock-out rounds as pool winners, but Sergio Aguero's late penalty distinguished any hopes of them pipping Borussia Dortmund, who ran out 4-1 winners over Ajax, to top spot.
"On two occasions I finished second in the group stage, I won the Champions League," the Madrid coach added. "I finished behind Real Madrid with Porto and we won, and with Inter I finished behind Barcelona and won.
"The other times I finished first, I never won the competition. My experience proves that it doesn't mean so much.
"I think the teams that finished first did well, but after that they are waiting for an opponent who, in principle, is easier for them to overcome, only to discover that they get Real Madrid in the draw."