The scoreline was goalless from the first leg of the last-16 tie in Seville but a quickfire brace from Wissam Ben Yedder in the second-half silenced the Old Trafford faithful on Tuesday night.
Romelu Lukaku pulled a goal back for the Red Devils in the 84th minute but it came too late and the Belgian’s effort proved to be merely a consolation.
Mourinho lost his cool with a Spanish reporter during a particularly prickly post-match press conference but kept his composure after giving his players a dressing-down.
The Portuguese asked for permission to enter Sevilla’s dressing room at Old Trafford before passing on his best wishes to Vincenzo Montella’s squad.
According to the BBC, Sevilla’s players were so impressed with Mourinho’s grace and humility that they responded with a round of applause.
Mourinho revealed that he was ‘happy’ his players were disappointed with the result as it would serve them well in the future.
He told MUTV: ‘Of course everybody is sad, as I told the players in the dressing room, I’m happy with this sadness, I’m really happy with that.
‘But we have no time to be sad for a long time, we have a match on Saturday.
‘The players are back to the training ground, and focusing on an important match on Saturday as I was saying these two matches against Sevilla and Brighton, if you win you’re in, if you’re lose you’re out.’