The mascot mocked Zaha by diving in front of him at the end of a Premier League fixture on Boxing Day in 2016 after the forward was earlier booked for simulation in the penalty box.
Zaha was also booked for going down too easily in a league meeting between the two clubs in April, leading to the 25-year-old Ivory Coast international to bemoan how he was being portrayed as a diver.
“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, because that’s not what football matches are about,” Hodgson said.
“That’s not what football matches are about. If it’s provoking the crowd into looking for something that is not there then it should be stopped.”
The then Palace boss Sam Allardyce criticised the comedy dive of Harry the Hornet, describing the action as “out of order”, but the Football Association decided against taking any disciplinary action.
Zaha appeared to take the cheeky act in light-hearted fashion as he sent a post on Twitter to the mascot, Gareth Evans, with a thumbs up and a picture of judges holding up scorecards.
“Wilf Zaha does not dive for penalties,” Hodgson said of his player.
“He gets knocked over sometimes. Sometimes he gets unbalanced without it necessarily being a penalty because he runs with such speed and he has such agility with the ball.
“I would be very disappointed if a 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.”