The Red Devils offered their Armenian playmaker a rare start in a third-round meeting with the Rams at Old Trafford.
Mkhitaryan has struggled for game time of late, with a tumble down the pecking order having sparked talk of a possible transfer during the January window.
Mourinho’s actions against Derby have further fuelled that speculation, with the United manager admitting that he was wrong to give a 28-year-old talent short on match sharpness just 45 minutes.
The Portuguese, who saw Romelu Lukaku grab the second goal in a 2-0 win having replaced Mkhitaryan at the break, told reporters: “[It was] unfair [to take Mkhitaryan off] and I told him that at half-time.
“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 also failed to see the game out in his last start, against Southampton on December 30.
He has struggled to convince Mourinho of his worth of late, with his value having been questioned on the back of a dip in form.
"I was not happy with his last performances," Mourinho said in November. "I'm not speaking about one or two, I'm speaking about three, four or five.”
The former Borussia Dortmund midfielder had opened the 2017-18 campaign in some style, with a flurry of assists, but his contribution has started to wane after being given less of an opportunity to make an impression.