The 20-year-old made his debut for the Premier League champions, hitting the post late on as David Moyes lost his first match in charge to Thailand All-Stars.
Goal reported in June that West Ham were eyeing a loan swoop and former club Crystal Palace ruled out a return, while Moyes has previously insisted Zaha will be afforded opportunities at Old Trafford and the youngster is keen to prove his worth.
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"I have moved away from most of my family and friends but it's progress. Everyone understands that. I wanted to make the move here because it's what is best for my career."
Zaha's arrival at Old Trafford was delayed following his involvement in England Under-21's failed European Championship showing, and he admits his arrival was slightly daunting.
"I just stayed in my corner of the dressing room really and looked about and tried to get used to everyone. Everybody jokes around in the changing room and all that kind of stuff so it was just enjoyable really. I was a bit nervous coming in but everyone is cool so it was nice.
"I would've preferred starting with everyone else [the previous week] so I could make a good impression and put in a good effort so I'm just glad I was here before the [Asia] tour started."