"I expect more from my players," Mourinho, who made eight changes to the side that beat Fulham 4-1 in the league last weekend, told reporters.
"Especially players that week in, week out, they ask why they don't play, why they don't start... it was a good match to play, without any kind of pressure, in a competition that everyone likes to play in."
Paul Pogba returned to the starting side after being benched for the last two Premier League games but the French international midfielder failed to seize his opportunity.
United then introduced striker Marcus Rashford, and midfielders Jesse Lingard and Ashley Young as they chased the game after falling 2-0 behind.
"In the end, my team improved when I made changes I didn't want to make, which is frustrating because I didn't want to play the three players I played in the second half," Mourinho added.
Defeat meant United missed the chance to top the group after leaders Juventus were surprisingly beaten 2-1 by Young Boys.
"Before the game I told the players that, if we win tonight and Juventus win, we did our job. If we don't win and Juventus don't win, we can blame ourselves," Mourinho said.
"But finishing second in this group is a success and I don't think that finishing first or second -- apart from a couple of clubs who are clearly much better than the others (means that) the draw will be significantly different."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by John O'Brien)
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