Mkhitaryan, 27, signed for £26m from Borussia Dortmund but was left out of the side repeatedly until recently.
But in his third successive start, he struck his first United goal in their Europa League win over Zorya Luhansk.
"He worked really hard physically, tactically and we know the talent is there," said Mourinho, 53.
Mkhitaryan was a substitute in United's opening-day win at Bournemouth but was hauled off at half-time in his first league start at Manchester City in September and did not feature again in the Premier League until late November.
During the Armenian's absence, Mourinho said the midfielder needed time to adapt to the English game and called on the 2015-16 Bundesliga players' player of the year to "do more".
"He has a strong mentality," Mourinho added. "He was very determined to fight against his difficult adaptation, and he's doing that in the best way.
"He fought to improve tactically, he fought to improve physically, and now he is playing good in the Premier League, good in the Europa League and the EFL Cup, and now evolving a bit more happiness for him, so I'm very pleased."
Mkhitaryan's excellent run and finish put United ahead in Ukraine and Zlatan Ibrahimovic's late strike sent them into Monday's last-32 draw as Group A runners-up behind Fenerbahce.
Mourinho rested several players including goalkeeper David De Gea and his stand-in Sergio Romero was visibly surprised when a firecracker landed in his six-yard box during the first half.
"Maybe Uefa is not happy and maybe Uefa now takes some money from Zorya, which I think Zorya doesn't deserve," added Mourinho.

The department alleges that the funds were "misappropriated" and though it did not name PM Najib Razak directly, he is identifiable in the suit as someone whose account allegedly received huge sums.
He has in the past denied wrongdoing.
Mr Najib set up 1MDB in 2009 to turn Kuala Lumpur into a financial hub, but it missed debt payments in 2015.
The US justice department alleges the "misappropriated" funds financed lavish lifestyles of "multiple individuals including public officials".
There is no allegation that Mr Najib spent any of the money but people close to him are accused of using billions of dollars to buy jewellery, art and luxury properties; pay gambling expenses; and hire musicians and celebrities to attend parties.
Malaysia's 'most investigated' company
1MDB: The case that's riveting Malaysia
The court papers, filed in Los Angeles, allege that money was laundered through accounts in the US. If successful the US justice department would seize assets, including property in the US, UK and Switzerland.
The $1bn would only make up a proportion of the money that was allegedly diverted, which comes to more than $3.5bn (£2.6bn).
Mr Najib's stepson, Riza Aziz, is named in the court papers, which were filed in Los Angeles. Mr Riza produced the Leonardo DiCaprio film The Wolf of Wall Street.
A Malaysian financier and two Abu Dhabi government officials are also among those named.
A spokesperson for the prime minister said: "The Malaysian Government will fully co-operate with any lawful investigation of Malaysian companies or citizens in accordance with international protocols.
"As the prime minister has always maintained, if any wrongdoing is proven, the law will be enforced without exception."
The fund started to attract attention in early 2015 when it missed payments for the $11bn it owed to banks and bondholders.
The Wall Street Journal (ESJ) reported it had seen a paper trail that allegedly traced close to $700m from the troubled fund to Mr Najib's personal bank accounts.
1MDB said in a statement last year that it had never given money to the prime minister and called the claims "unsubstantiated". It has repeatedly stated that the company has assets worth more than its debts.
Mr Najib has denied taking money from 1MDB or any public funds.
Manchester United boss Jose Mourinho has praised Henrikh Mkhitaryan's fighting qualities in adapting to his summer move to Old Trafford.
[NEXT_CONCEPT]
The US Department of Justice has moved to seize more than $1bn (£761m) from Malaysia's state fund 1MDB.