United boasted two-thirds of the possession and had three times as many shots as their opponents at Wembley, but Eden Hazard's first-half penalty ultimately proved to be the difference as Chelsea lifted the trophy.
United struggled to turn their dominance of the statistics into clear chances on the pitch, but Herrera is adamant that his side deserved to have won the game.
"Really disappointed because I think we were the better team by far," he told reporters.
"I think we controlled the game. We played really well, we created a lot of problems and we were the better team.
"But in football, not always the better team wins the game, so I can congratulate them and hopefully we can come back next season."
The defeat was the first United boss Jose Mourinho has ever experienced in a domestic cup final in England.