A first-half penalty from Eden Hazard proved to be enough for Chelsea to get one over on their former boss and lift the trophy for an eighth time, despite United enjoying 66% possession and 18 shots to Chelsea's six.
It was not until the second half that United really began to put Chelsea under any serious pressure, though, and Mourinho suggested that the absence of Romelu Lukaku - only deemed fit enough for the bench - hurt his side.
"I congratulate them because they won but I don't think they deserved to win. I congratulated them. I am Manchester United manager and I have to be respectful, not just because they are my previous club but because they are the opponents today but I think we deserved to win," Mourinho told BBC Sport.
"I am quite curious to know what you say or what people write because if my team plays like Chelsea did I can imagine what people would say. I am quite curious. It was a bit hard for us to play without Lukaku against a team that defends with nine players. You need that presence. Every defeat hurts but I go home with the feeling we gave everything. No regrets.
"Chelsea are not stupid. They know our team without Lukaku or [Marouane] Fellaini does not have a presence so putting eight or nine players in front of the box they knew they would be dominant in that direct football. We tried everything by other ways but they had a huge block of compacted players. The image of the game is that David de Gea did not touch the ball. He touched the ball in the net."
The defeat is Mourinho's first from his six English cup finals.