After seemingly doing the hard work by battling to a goalless draw away to the La Liga side, United went into the second leg at Old Trafford as favourites to progress.
However, Sevilla had other ideas and two quick second-half goals from Wissam Ben Yedder gave them a shock 2-0 lead, leaving the Red Devils with a mountain to climb.
Romelu Lukaku pulled one back late in the game, but it wasn’t enough for the three-time winners of Europe’s top club competition.
United have not made the quarter-finals of the Champions League since 2014 but Mourinho was defiant when asked about his side’s approach to the game.
Mourinho said: “We had good periods. I wouldn’t say we had great control of the game but I couldn’t say my players had something wrong in terms of their attitude and their intention to play.
“We tried since the first minute to be aggressive and intense and I could find some similarities between the beginning of this game and against Liverpool last weekend, but then we didn’t score and Sevilla progressively kept the ball and were quite confident having the ball and hiding the ball from us and controlling the game well.
“The first goal will be always important in this match not just because of the first leg result but also because of the style of the match.”
The Old Trafford club become the second Premier League casualty of this season’s Champions League, after Tottenham, who lost to Juventus last week.
The FA Cup is the only hope of a trophy for United this season, barring a monumental collapse in form in the league from leaders Manchester City, but Mourinho remained philosophical on his side’s chances and the remainder of the season.
He added: “A fantastic team like Tottenham has to do exactly the same as us.
“Liverpool has the Champions League but doesn’t have the FA Cup. That’s football, that’s life. We lost and tomorrow is another day and Saturday is another match.
“Every player is sad and they don’t hide that sadness. That is something that pleases me because I feel exactly the same but we have no time for dramas because on Saturday we have to work as we have an important match.”