The 18-year-old had a goal disallowed in the 70th minute after his shot came off Zlatan Ibrahimovic who was offside, and though his energy and pace could not secure a result for United, his manager praised him as a potential game-changer.
"For me the next big game is against Feyenoord and the next game (Rashford) is going to play," Mourinho told reporters.
"I trust him completely. I know his future will be absolutely brilliant.
"Normally, people look to the football talent but personality at his level is very important and he was showing that last season -- he was showing that immediately."
Rashford, who scored on both his Premier League and Europa League debuts for United last season, is by far the most exciting graduate of United's academy in years.
The teenager also scored three minutes into his first senior start for England against Australia in May and bagged a hat-trick on his England Under-21 debut last week.
Mourinho said he viewed Rashford as an out-and-out striker, but conceded the forward had offered his team a better outlet when deployed on the wing against City than established wide players such as Henrikh Mkhitaryan and Jesse Lingard.
"I felt City had the fragility on the sides and the kid could give us in the second half on the sides what we didn't get with Henrikh Mkhitaryan and Jesse Lingard in the first half," Mourinho added.
"The kid gave us what we had needed in the first half."
(The story was refiled to fix a typo in the seventh paragraph)
(Reporting by Simon Jennings in Bengaluru; Editing by Ian Ransom)
