Harry the Hornet mocked Zaha, 25, by diving in front of him after the Palace winger was booked for simulation during a 1-1 draw on Boxing Day in 2016.
Zaha said there was an "agenda" against him after he was also shown a yellow card for diving at Watford in April.
"Zaha does not dive," said Hodgson.
"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.
"And certainly if it's provoking the crowd into looking for something that's not there, it should be stopped."
Former Palace boss Sam Allardyce said Harry the Hornet was "out of order" after the incident in 2016 but the mascot avoided disciplinary action by the Football Association.
Zaha reacted angrily as he left the pitch at the time but appeared to see the funny side later on, tweeting Gareth Evans, who plays Harry the Hornet, a message with a thumbs up and a picture of diving judges holding up scorecards.
After the goalless draw at Vicarage Road in April, the Ivory Coast international said he felt people were trying to get him banned and Hodgson again backed his player on Friday.
"Wilf Zaha does not dive for penalties," said the former England boss. "He gets knocked over sometimes and sometimes he gets unbalanced without it being a penalty or a foul, because he runs at such speed and has such agility with the ball.
"But of course teams try to take every advantage they can.
"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."
Watford v Crystal Palace: Roy Hodgson tells Harry the Hornet not to mock Wilfried Zaha
24 August 2018
Crystal Palace boss Roy Hodgson has warned Watford mascot Harry the Hornet against "disgraceful" provocation of Wilfried Zaha in Sunday's Premier League game at Vicarage Road.