The Belgian striker, Romelu Lukaku and Marcus Rashford scored as 67,401 at NRG Stadium watched United win 2-0 in the first Manchester derby outside England.
New signing Lukaku beat City keeper Ederson Moraes to Paul Pogba’s pass on 37 minutes. Then Rashford drove in Jesse Lingard’s pass two minutes later.
“I’m really pleased,” said Mourinho.
“I’m sure Pep [Guardiola] is the same. The most important thing was to give the players high quality training.”
City came close to reducing the deficit when Fernandinho’s long-range shot was tipped over by Sergio Romero. And City boss Guardiola was delighted with the performance of 17-year-old midfielder Phil Foden, who was making his first-team debut.
“I don’t have words to describe what I saw,” Guardiola said. “His performance was at another level. He loves the club. He is a City fan. He is a gift.
“Maybe this season he will stay with us because he is special. Creating chances, always in the best position.”
It was the first derby since the bombing at Manchester Arena on 22 May and both teams wore shirts with the distinctive ‘worker bee’ logo, which will be auctioned off to raise money for the victims.
Analysis – who is Phil Foden?
The ‘gift’ Pep Guardiola spoke of after the game comes from the Manchester City-supporting heartland of Stockport.
Foden has been at the club in some capacity since he was six and scored in last season’s FA Youth Cup final against Chelsea.
He also netted for England in their European Under-17 Championship final defeat by Spain in Croatia, where he started every game.
Foden is also a fine passer of the ball and has an uncanny ability to get past opponents.
He is probably too small to be considered for Premier League duty in his favoured central midfield role at present but it is easy, looking ahead, to see him having a similar kind of impact at City as David Silva.