Los Blancos had already won the first leg 3-2 and successfully held on to their lead in the return clash and kept a clean sheet, much to the delight of Mourinho.
"We defended very well and our opponent hardly had any chances to score. We've scored eight goals in our previous two games and people accused us of not defending well. We gave a serious, pragmatic and practical performance," Mourinho told reporters.
"We didn't give a brilliant performance with the ball, but we 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."
Real Madrid will meet Barcelona in the quarter-finals of the Copa del Rey if the Catalans successfully defend their four-goal advantage against Osasuna on Thursday.
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