Antonio Adan, widely considered inferior to the club captain, was chosen to start between the sticks by the Portuguese coach.
The defeat ensured that los Blancos are now 16 points behind Barcelona in La Liga, but Mourinho defended his decision and claimed he was merely picking what he saw as the strongest starting line-up.
"I have a clear conscience. Trying to make the best team for each match," he told Marca.
The former Chelsea, Inter and Porto boss added: "Losing makes you realise what others suffer."
With the league title now looking almost impossible to retain, Mourinho will hope his side fare better in the knockout stages of the Champions League.
The Spanish giants face Manchester United in one of the highlights of the last 16 draw, which also sees Barcelona drawn against AC Milan; Valencia up against Paris Saint-Germain; and Malaga tasked with surpassing Porto.