Zaha was Sir Alex Ferguson's last signing as United manager before he retired.
The 28-year-old is adamant that David Moyes was "not keen" on him, but insists he would "impose himself more at the club" if he were able to turn back time.
Speaking at the Financial Times' Business of Football summit, he said: "The only thing I would have done differently is impose myself more at the club, to my team-mates, to everything. I've said before in interviews, I was just a shadow of myself because it was all new to me.
"Going there, and I'm thinking it's all going to go well and then being hit with a manager that's not keen on you and being away from home, I was a bit shell-shocked, like 'what do I do now?'
"Even then, I didn't go to the manager's office and ask why I wasn't playing, I didn't have the confidence to do those things. It was just accepting and hoping he'd change his mind. Just hoping.
"I don't believe in just hoping, I feel like the work I put in brings the results. I'm so much more front-foot now. The experience, I'm older now and I would have imposed myself on that team a lot more."
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