The win in the first leg of the Champions League quarter-final at the Santiago Bernabeu was actually Real's first clean sheet in Europe this season.
Mourinho insisted that, unlike the local media, Real took the threat from Galatasaray seriously.
"I think we played seriously, the Spanish press are not so respectful to Galatasaray but we are respectful of them," he told Sky Sports.
"We knew they had a good team, they had fantastic strikers, they had danger in every attacking action and we prepared very well for the match by the defensive point of view - we defended better than we attacked.
"In the attacking third I think we lost the last ball, the last pass we had easy transitions - 3 on 3 and 3 on 4, and we could have scored more goals, but I think by our defensive point of view we had a good analysis of the situation and the team played very well."
Mourinho admits a goal from Real in Turkey in the second leg next week would put the game beyond Galatasaray.
"If we score a goal they have to score five, the result is very good but in football I have seen so many incredible things and nothing can surprise me and Istanbul is a difficult place to play," he added.
"They have players with a lot of experience, great character and personality and they will fight very hard against us and we know we have to go there very seriously as that is the only way to get through."
Mourinho also denied that he told Sergio Ramos to deliberately pick up a late booking which, although ruling him out of the second leg, means he has a clean slate ahead of a prospective semi-final double-header.
"I lost Xabi Alonso and I was thinking about playing Pepe in midfield in Istanbul and his yellow card leaves me with a problem to resolve," he insisted.
Mourinho also admitted he spent time with two of his former players Wesley Sneijder and Didier Drogba at the final whistle.
"I was with them at the end of the match, him [Drogba] and Wesley - they are family - they weren't during 90 minutes but they are family."