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.