Eden Hazard scored the only goal of the game as Chelsea lifted the trophy for an eighth time at Wembley, although United ended the match with 66% of the possession and having registered 18 shots on goal to the Blues' six.
Mourinho insists that he is "happy" with his players and believes that his side were in control of Chelsea for the most part, with the critical exception of Hazard's winner from the spot.
"Every defeat hurts, but for me personally the ones that hurt less is when you give everything and you go without any regrets," Mourinho told reporters at his post-match press conference.
"I prefer to lose like today than lose like we did at, for example, Newcastle. I leave my players happy with them. For me that's really important.
"When you play against a team so predictable it's quite easy to adapt to it. I thought we wouldn't concede any goal in this match. But of course Hazard is a very good player and he created a penalty."
Before today Mourinho had won all five of his domestic cup finals in English football.