The 20-year-old completed a £17m move to the Red Devils last week before he was loaned back to Championship club Palace until the end of the season.
"I'm glad I'm back on loan as I didn't want to leave the job unfinished. Being with the team is like a family," Zaha told reporters.
"I just want to get back to doing what I do best and get us back to the Prem. That's what I've got my mind set on."
Palace are currently in fifth place in the Championship table.