The Premier League side immediately loaned the England Under-21 international back to Crystal Palace as part of the deal, but Zaha told the Daily Mirror that he is determined to justify his transfer fee when he joins up with the Red Devils.
He said: “It means a lot to me because, for all the good stuff I hear about me, people saying I’m a good player, there are many that say I’m overrated.
“So this is a great chance for me to show what I’m all about and why I have got to where I am now.
“It will be more practice for me this summer for when I go into pre-season training with Manchester United.
“It’s a chance for me to better myself in different ways and to go out and prove myself on a big stage.
“I’m not sure I will ever get used to it. I’m going to have to try and get used to it and go and play my own game.”
Zaha, who scored his first goal for the England Under-21 team on Thursday, added: "I do feel the pressure and the hardest thing about being a footballer is to cope with it.
“I just get my head down and tell myself I’m there for a reason. Every time I go on the pitch I have to prove myself.
“It has been a dream being involved in the international set-up. I wanted to push on from just club football but being part of the whole set-up is incredible."The forward, who has been deployed as a winger for Crystal Palace but a striker for England, admitted that he is looking up to 23-year-old Gareth Bale, who has dramatically helped Tottenham push for a Champions League place next season.
“I have played out on the wing for Palace, but I used to play up top for the youth team. I’ve enjoyed it really. Gareth Bale has been ridiculous this season so if I could play anything like him I’d be very happy."