Mkhitaryan played the first 45 minutes as Man United opened their pre-season campaign with a comfortable 2-0 victory over Championship side Wigan Athletic at the DW Stadium.
Mourinho, who brought the 27-year-old to England from Borussia Dortmund, has paid tribute to the qualities of his summer signing, calling him "magnificent".
"[Henrikh] Mkhitaryan is a top-class player and currently at the best stage for a footballer – 27/28 years old," Mourinho told MUTV. "He is magnificent the way he thinks about football, he thinks very quickly and it's so sweet how he touches the ball. He can play in different positions behind the striker. He doesn't have the sharpness yet but he is performance was very positive."