An own goal by Cristiano Ronaldo saw Los Blancos slump to their fifth defeat of the season, meaning that they remain four points behind second-placed Atletico Madrid having played one game more.
Mourinho, whose future at the Bernabeu is in doubt, blasted his players for their first-half performance.
"When we win and everyone plays well it's the result of self-management, but when we lose it's the responsibility of the coach," Mourinho told reporters.
"So we didn't play well today, we weren't ourselves, so now I'm the one responsible.
"We didn't manage a draw and the result bothers me. It bothers me also that in the first half we were terrible and even if we tied in the second half, there would have been very little to be satisfied about."
Real play host to Sevilla next Saturday.