The 20-year-old joined the Red Devils in January but was instantly loaned back to the Championship outfit for the remainder of the season.
Freedman, who was in charge of the Eagles when Zaha established himself at Selhurst Park, believes that the forward must be allowed to adapt by the Premier League champions.
"It took him eight games to establish himself in the Palace first team and eight to 10 games later he was the best player," said Freedman.
"I have no doubt he will take time to settle in but when he does he will show the talent that he has.
"I know his character and he won't be fazed, David Moyes will see that day in and day out."
Zaha has been linked with a loan move away from United.