Although Romelu Lukaku struck back with six minutes to go, United - who drew 0-0 in the last-16 first leg - would have needed two more goals to counter Sevilla's away strikes and ultimately fell short.
"I think the first goal was always going to be important, not just because of the first-leg result but also the profile of the match," Mourinho told BT Sport after the game.
"We tried to be aggressive and intense from the first minute. We didn't score and Sevilla progressively kept the ball, and they controlled the game well.
"We had good chances to score, but they scored one goal and from that moment everything became much more emotional. The second goal made it impossible.
"We had good periods, we didn't have great control over the game, but I can't say there was anything wrong with my players and their intention to play.
"That's football, we lost, but tomorrow is another day and Saturday is another match. I'm pleased the players aren't hiding their sadness, but we have no time for drama."
United return to action at the weekend with an FA Cup sixth-round tie against Brighton & Hove Albion at Old Trafford.