Karim Benzema struck the only goal of the game in the 72nd minute to hand Los Blancos a 4-2 aggregate win, but while it is normally Real's deadly attack that gets most of the attention, Mourinho feels it was at the back that his team did their best work against Malaga.
"We've scored eight goals in our previous two games and people accused us of not defending well," Mourinho told the club's official website.
"We gave a serious, pragmatic and practical performance tonight [Tuesday].
"We defended very well and our opponents hardly had any chance to score."
While Mourinho admits their overall performance over Malaga over two legs probably was not Real at their best, he did give credit to their opponents whom he believes were clever in their approach.
"We didn't give a brilliant performance with the ball, but we nevertheless reached the next round against a solid side that played intelligently in both legs.
"It would have been even harder if we hadn't scored the goal. We made a great effort to win.
"My objective was for us to score in the first half to force Malaga to take risks, but we didn't manage to.
"We were too comfortable in the first half and played a slower game than we're used to. We tried to speed things up later on."
One of Mourinho's few problems this season has been to choose between Marcelo and Fabio Coentrao, who both play best when deployed at left-back.
However, both played together in the second half and combined well, leading Mourinho to suggest they both have different qualities they bring to the side.
"Marcelo started the second half as a left-back, but when [Salomon] Rondon took to the pitch he forced my full-back to defend inside.
"Fabio defends well there and Marcelo moved further up to favour our counterattack."
Real are next in action on Saturday when they travel to play Real Mallorca.