Pardew was given the boot on Thursday following a nightmare 2016, with Sam Allardyce replacing him in the Selhurst Park hotseat.
Zaha was brought back to south-east London on a permanent deal by the former Newcastle boss in 2015 following a frustrating spell at Manchester United.
The winger netted 11 times in 82 games under Pardew, but he was unable to save him from the sack.
However, Zaha took to social media to thank his old boss and wish him well.
He tweeted: “Sorry to see Alan Pardew go but wish him the best of luck in the future.
“[He] Believed in me when many didn’t and helped me massively as a player and a person so I’m very thankful.”