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."