A second-half strike from Javier Camunas earned 17th-place Osasuna the spoils in a hard-fought came at the Reyno de Navarra stadium and consigned Madrid to only a second league defeat of the season.
Mourinho said after the game: "My players have done their jobs with dignity and I have nothing to reproach them for, they fought to the end. We lost three points that we didn't deserve to lose.
"Osasuna are a tough team and the crowd was fantastic. I don't think many teams win here. We had opportunities to score in both halves, but we haven't done it. And if the opponents score first it is very difficult. Congratulations to Osasuna."
The Portuguese added: "This is our second defeat in La Liga and we are in a much more difficult situation with respect to first place.
"I always tell my teams that I don't like to gift games to the opposition, by not playing, not fighting or because we were relaxed...that wasn't the case. We lost against a team who gave it everything, and who had a week to prepare for the match."