The Armenian's latest opportunity to impress his manager lasted just 45 minutes as Mourinho replaced him with Romelu Lukaku following a goalless first half on Friday night.
Goals from Jesse Lingard and Lukaku secured victory for United but the Portuguese admitted after the match that he felt uncomfortable withdrawing Mkhitaryan despite the result.
"[It was] unfair [to take Mkhitaryan off] and I told him that at half time," Mourinho told reporters. "I didn't like what I did. He didn't deserve it, he was playing well, he wasn't playing bad.
"He had a couple of missed passes but he was playing well and giving a good dynamic to the team.
"My feeling was just that [Marcus] Rashford is not going to score a goal and because of that I'm not going to lose time and I'm going to play Romelu, so then I had to sacrifice a player.
"Mkhi was the one that I sacrificed but it's something that I don't normally do but I did at half time and apologised to him in front of other people because he didn't deserve it."
Mkhitaryan has made 22 appearances for United this season but has clocked up just over 1,300 minutes of action.