Adan was chosen ahead of Iker Casillas for the second consecutive game, but was sent off after just six minutes.
"I said to him before the match, and the Malaga match too that the whistles that he hears are for me, not for him," said Mourinho.
"The fans have no problem with Adan, or the press either. They have a problem with me and my decision. My personal opinion is that Adan deserves much more respect. He has been at Real Madrid for 16 years, he trained at Real Madrid, he comes from a home of Real Madrid fans, born in Madrid. Why doesn’t he have a right to be happy? You have transformed a problem and an attack on Mourinho into a lack of disrespect towards Adan."