Jose Mourinho apologised to Henrikh Mkhitaryan for taking him off at half-time of Manchester United's FA Cup win over Derby County on Friday.

The Armenia international, who was an unused substitute in the 2-0 Premier League victory at Everton on Monday, was replaced by Romelu Lukaku at the break with the game goalless.

United went on to win the third-round clash 2-0 thanks to late goals from in-form Jesse Lingard and Lukaku, who was making his first appearance since suffering a head injury in the goalless draw with Southampton on December 30.

Mkhitaryan has struggled badly for form in recent months and has found his playing time limited, but Mourinho insists he only took off the former Borussia Dortmund man for tactical reasons.

"[It was] unfair [to take Mkhitaryan off] and I told him that at half-time," the United manager said. "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. Micki 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."

United missed a host of chances, with Rashford twice hitting the post and Derby goalkeeper Scott Carson making several fine saves, before Lingard broke the deadlock in the 83rd minute with a sublime half-volley.

Mourinho says the England international's form shows he feels "like a fish in the water" and has backed Rashford to recover his own goalscoring touch.

"It was an amazing strike," he said. "He's in a clear evolution. I think he's comfortable in the positions he plays, I think he's improving with the progressive style of play of the team.

"He's playing progressively in a different way which makes him feel even more like a fish in the water and he's in this moment where things go well for him.

"He's the opposite of Marcus because, in training, he [Marcus] is scoring unbelievable goals but is coming to matches and missing unbelievable chances, hitting the post and the goalkeeper saves, so clearly the players have these moments.

"I'm not worried with Marcus because the good moment will arrive and Jesse, if a negative moment arrives, I don't think he will lose this stability that he's showing. He's mature, he understands the game better, so clearly he's becoming a real player."

Mourinho also praised Lukaku for his quick recovery, after the Belgium striker scored United's second in the 90th minute at the end of a counter-attack he started on the halfway line.

"He is another example of what a Manchester United player has to be," Mourinho added. "A great professional, amazing desire to play. We had to stop him playing against Everton, three days later he is here and working the way he is working and showing his desire, his commitment, so I am really happy for him."