Sergio Sanchez and Martin Demichelis scored in the 10th and 29th minute respectively to hand unfancied Malaga a shock 2-0 lead at the Santiago Bernabeu going into the break.
However, following a severe tongue lashing by Madrid tactician Mourinho, the nine-time European champions got their act together and goals from Sami Khedira, Gonzalo Higuain and Karim Benzema turned the tie around for the home side, culminating in an eventual 3-2 win.
"We made things difficult for ourselves in the first half, but we played differently after half-time, looking for open spaces and a victory," Casillas explained to the club's official website.
"Real Madrid will always try to do their best. We gave two goals away because we weren't experiencing many problems and we gave a good performance."
"We'll have the advantage in the return leg, but we cannot afford to relax."
The second leg of their Copa del Rey last-16 clash will be decided at Malaga's La Rosaleda turf next week.