Zaha, 20, went off the boil after United signed him, scoring only one goal in the second half of the regular season.
But he was back to his blistering best in the play-offs as his double earned a 2-0 second-leg win at Brighton to send Palace to Wembley.
Hilaire told The Sun: “After being signed by the biggest club in the world you cannot blame him for thinking: ‘That’s my season done, roll on next year’.
“It arguably took the play-offs against one of Palace’s biggest rivals to fire him back to his best.”
Hilaire reckons Zaha could go on to become a global superstar at United.
He said: “I compare him to Cristiano Ronaldo — he’s got very quick feet and an eye for goal.
“I just hope he gets the chance at United to show what he can do.”