The 20-year-old moved to Old Trafford for £15million in January 2013 before moving back to Selhurst Park on loan until the season finished.
He subsequently won the Championship's Player of the Year award after helping guide the Eagles back to the Premier League via the play-offs.
The England international rejected any suggestions he may be loaned out again by new United manager David Moyes after firing a late equaliser in the 2-2 friendly draw with Cerezo Osaka in Japan.
"My own target for my first season in Manchester is to be able to get minutes," Zaha said.
"I don't want to go out on loan or anything. I just want to play when I get the chance."
Zaha accepted the quality of his team-mates would put a premium on the minutes spent playing for the league champions' first team and added: "That is the gamble I had to take.
"I am prepared to take that gamble. I enjoyed my time at Palace but I am at Manchester United now.
"There are bigger players than me here, so getting minutes will just do me fine."
Moyes was certainly impressed, particularly as Zaha's late intervention staved off a third defeat in four games.
"Wilfried has done well," said the United boss. "He has been quite quiet because he is still getting to know everybody, but he has had an impact in the games.
"We want to try and bring him along nicely. Tonight will help because he showed the players that he can make things happen.
"We want all players at Manchester United to score goals and he has come up with an important one."