Mourinho, whose side remained 15 points behind La Liga leaders Barcelona, was gracious in defeat.
"I think the result is fair," the Portuguese said on realmadrid.com.
"There have been too many defeats. Granada did their job, they scored their goal.
"They defended in the second half with all of their heart and soul. They have a new coach, new players and had a great night of football here with Real Madrid in front of them.
"They did everything that they could to get this result.
"We should have scored a goal but because of the great effort that Granada made, I think that the three points have gone to the team that deserved them."
He added: "The buck stops with me. You lot (the media) always say that same thing. When we win and we play well then it happens on its own, but when we don't it is the coach's responsibility.
"Today we lost and did not play well. Today it didn't happen on its own - today I'm the one responsible."