Mourinho caused a major stir after choosing to start with back-up goalkeeper Antonio Adan for the Primera Division clash at La Rosaleda in place of captain and long-serving number one Casillas.
Mourinho said after the match, which Madrid lost 3-2 to slump 16 points behind leaders Barcelona, that his decision was "purely technical".
Speaking ahead of a charity match in Madrid, Casillas told La Sexta television: "The coach decides which team he thinks is best for each match and you need to accept the decision.
"I'm not used to being a substitute, but above Iker Casillas or any player is the team. What I need to do is continue training and try to recover the confidence of the coach."
Casillas, who has won a host of titles with Madrid and captained Spain to the World Cup and back-to-back European Championships, added: "I feel good, but it is the coach who decides who plays. It will be a nice battle with Antonio. There is a healthy rivalry between us.
"Throughout the week I could sense that I wasn't going to play but it's not a setback. The important thing was that the team won in Malaga to cut the gap to Barca and Atletico.
"Mourinho didn't explain anything to me. He doesn't do it when I play, nor when I don't."
Mourinho, meanwhile, insists he does not regret dropping Casillas for the match.
Speaking after arriving at Lisbon airport on Sunday, the Portuguese coach was quoted as saying by AS newspaper: "Casillas? I have a clear conscience. I try to choose the best team for every game."
The loss to Malaga was Madrid's seventh of the season in all competitions, which is already more than they suffered in the whole of the last campaign and has seen the pressure build on Mourinho.
The former Inter Milan and Chelsea boss was defiant following the game when answering questions about his future, insisting he had no intention of quitting Madrid and did not fear for his job.
However, he does feel the gap to Barca is now insurmountable.
Madrid defender Sergio Ramos also concedes their title is now virtually lost but has demanded the team keep on fighting.
"Once again we have dropped important points, despite the team playing well in the first half, in which we had chances to score but we didn't have any luck," Ramos said on the Madrid website.
"We shouldn't think about the league leaders or anybody else. We should only think about ourselves.
"We must be self-critical and La Liga is now very difficult, practically impossible, but we need to keep on fighting.
"When we lose many conclusions are drawn, but it is when we must use our heads the most."
Regarding Mourinho's decision to omit Casillas, Ramos added: "Iker is the captain and he will continue to be the captain because he is a great goalkeeper."