Watford's mascot performed a comedy dive in front of Zaha when the winger went to Crystal Palace fans after the final whistle.
The Palace winger had been booked for diving in the second-half of the Premier League clash -- former England manager Allardyce's first in charge of Palace since replacing Alan Pardew.
The hosts' mascot -- dressed as a Hornet after the club's nickname -- performed a comedy dive in front of Zaha when the winger went to his fans after the final whistle.
Zaha had also had a penalty appeal turned down late in the match when he went down in the box.
"The mascot is out of order, isn't he? If someone is diving, they don't get that angry," fumed Allardyce.
Allardyce, who had to step down as England manager after just one match when he made ill-judged remarks to undercover reporters earlier this year, said he didn't know whether Zaha was being punished by referees because of his reputation for going down too easily.
"You'll have to ask the referees, ask (referees' chief) Mike Riley. If they are refereeing on reputation and not fact or incident, that's a black mark against them."
Zaha is reportedly in a tug of war between the Ivory Coast and England who both want him to play for them.