Goals from Chris Smalling, Juan Mata, Marcus Rashford and Paul Pogba's first for the club gave the hosts a 4-0 half-time lead before Demarai Gray scored spectacular consolation for the reigning Premier League champions.
Speaking about Rooney, who was dropped to the bench, Mourinho told Sky Sports: "He's a big player for me, a big player for United, a big player for this country.
"He's my man, I trust him completely. He's as happy as I am at this moment and that's the team.
"It was a very good performance. It's obviously a very good result, it's not easy to win against them and even more difficult to win in such a comfortable way.
"I think the team played very well, you score four goals, and the striker doesn't score a goal and I think the striker plays phenomenal.
"(Zlatan Ibrahimovic) Ibra played absolutely incredible in the way he started our pressure. My team as a team played very well."