The mascot saw an opportunity for 15 minutes of fame and dived onto the Vicarage Road pitch, behind Zaha, at the end of a 1-1 Premier League draw between the teams in December 2016.
Zaha has regularly been booked for simulation - he was shown a yellow card when the sides met again in April this year - although the Ivory Coast international appeared to see the funny side of Harry the Hornet's antics.
Posting on Twitter after that game, Zaha sent a message to the mascot with an image of judges holding up a series of scorecards.
But Hodgson, who was not in charge of Palace at the time of the incident, appears to be taking the matter far more seriously ahead of Palace's trip to Watford on Sunday.
"If you're asking me whether Harry the Hornet, who I presume is the mascot, should dive in that way, I think it's disgraceful," said Hodgson.
"Because that's not what football matches are about. And certainly if it's provoking the crowd into looking for something that's not there, it should be stopped.
"Wilf Zaha does not dive for penalties, he gets knocked over sometimes, sometimes he gets knocked over or unbalanced without it being a penalty or a foul, because he runs at such speed and has such agility with the ball. But he certainly doesn't dive.
"But of course teams try to take every advantage they can. You mentioned the mascot, I would be very disappointed if the Crystal Palace mascot was doing something like that to provoke the crowd against an opponent. And if I found out about it, I would stop it."
The man who wears the Harry the Hornet costume, Gareth Evans, seemingly responded to Hodgson's criticism on social media.
"Might buy some flowers for Sunday hmmmm," Evans wrote on Twitter. "Right well that’s made my weekend, how’s everyone else?"
The Eagle's boss was clearly stung by the Hornet's juvenile actions and it now seems unlikely that Gareth will be up to similar antics in his famous get-up when the two clubs meet this weekend.