Despite being heavy favourites at the start of the tie, United failed to perform across the 90 mins and were stunned by their Spanish opponents.
Wissam Ben Yedder came off the bench in the second half and scored twice to silence Old Trafford.
Romelu Lukaku scored late on to give United hope but it wasn’t enough as they limped out 2-1 on aggregate.
Fans streamed out of the stadium before full time, with players taking plenty of flack on social media for the performance.
But Mourinho refused to be critical of his players and said they did what they could to win.
Mourinho said: “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.”
Mourinho’s side now have only one realistic chance of winning silverware this season.
They are effectively out of the title race but face Brighton in the FA Cup quarter-finals on Saturday.
Reflecting on the Champions League defeat, which saw United record just four shots on target over the two legs, Mourinho admitted his game plan didn’t pay off.
“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,” Jose Mourinho said.
“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.”