Real looked to be coasting into the last four when Cristiano Ronaldo scored early on in Istanbul to give them a 4-0 lead in the tie, but Galatasaray roared back with three second-half goals in a 15-minute spell to test Real's nerves.
However, Ronaldo ended the brave Turkish team's chances of an unlikely comeback with his second goal of the night in injury time and, despite being given a scare by Galatasaray, Mourinho insists he had no time to feel any nerves.
"I wasn't getting nervous because I have no time for it," said Mourinho. "I am on the bench so I have no time to think or to feel it.
"Today is the kind of match where you have everything to lose and nothing to win. People think we are already in the semi-final and players had that feeling from the outside. I felt the team was ready to work hard and had the motivation to reach Wembley in the final."
Mourinho, who equalled Sir Alex Ferguson's record in reaching his seventh Champions League semi-final, was full of praise for the Galatasaray players and fans for making it so hard for his side.
"They are strong, strong mentally. They don't play against 11, they play 50,000 against 11 and it was hard for us," added Mourinho.
"We are there, in the semi-finals and that is what that matters.
"Now we have a semi to play, against a great team. We do not know which one yet, but they will be great. It will be hard but now is the time to enjoy ourselves and not to be nervous or afraid.