La Liga side fell to second league loss of season on Sunday
The La Liga giants suffered a 1-0 defeat in Pamplona and fell seven points behind league leaders and arch-rivals Barcelona.
"We lost three points that we didn't deserve to lose, but based on the way the opponent played, they also deserved a positive outcome," Mourinho is quoted as saying by Madrid's official website.
"The referee did a great job. My players couldn't have played out of this world based on the conditions.
"We didn't concede goals against Atletico, Sevilla or Mallorca. The team is playing well. One goal isn't reason to get dramatic, but we usually need to score.
"We had our chances. Benzema, Cristiano... But we didn't take care of business. Give credit to the opponent as well. I would rather lose like this. The opponent worked very hard for this outcome; my team did not give the match away."
The Portuguese continued: "This is our second defeat in La Liga and we are in a very difficult situation with respect to the first place team. I don't like to lose when you give the match away by not playing, not fighting or not being committed or focused.
"That is not the case. Tonight the other team played its heart out and had a week to prepare for the match. They played to the brink. Tomorrow is a new day. There will be another match and we will be there.
"Osasuna are a tough team and the crowd was fantastic. I don't think many teams win here. It's a small venue where you really feel the heat, and Osasuna is a defensive team that also plays well in attack.
"We had scoring chances, but we didn't finish. It is always a lot harder on small fields like this and when the opponent scores first. Congratulations to Osasuna."