The Santiago Bernabeu side fell 2-0 behind via goals from Mario Bermejo and Cristian Bustos before Cristiano Ronaldo pegged one back in the closing stages of the encounter, and Mourinho was left disappointed with his side's display.
"People are always entitled to their own opinion and have the right to criticize the coach. But perhaps it's not always the coach who shoulders all the responsibility... I took my responsibility and that's that," Mourinho said at a press conference.
"Some players have disappointed me, but you cannot expect me to comment on the performance of individual players.
"[Raphael] Varane was a true champion. He was injured toward the end, but still did more than some of the players who were fully fit."
Real Madrid will be looking to return to winning ways on Sunday when it hosts Espanyol.