The Armenian international has been unused for most of the season so far, despite the club parting with £26m to buy him from Borussia Dortmund in the summer transfer window.
Mkhitaryan has made five Premier League appearances, starting in just one, but in recent performances against Feyenoord in the Europa League and West Ham United in the EFL Cup, the 27-year-old has impressed.
On Wednesday night, Mkhitaryan was influential in United's 4-1 victory over West Ham in the quarter-finals of the cup competition, and he bagged two assists.
Mourinho has previously explained Mkhitaryan's absence, stating that the player was not physically ready to cope with the demands of English football, but it appears that the summer arrival has now settled.
"I'm so happy because today was against a Premier League team with Premier League qualities with Premier League characteristics," Mourinho told Sky Sports News.
"That showed clearly his evolution. Against Feyenoord we could think, 'OK it is a different profile of football' but today was against a proper and typical Premier League team and Micky could perform this way. So I'm really happy.
"We know the reason why we bought him and we were waiting for his adaptation and it looks like it's coming."