The Eagles rejected a £3 million bid for the England Under-21 international in the summer, and the winger had also attracted interest from fellow Championship club Bolton Wanderers.
This week Martinez labelled Zaha as a player with "tremendous potential" which riled Parish, who retaliated by also criticising the way the club "nicked" Victor Moses in January 2010.
"Some fascinating quotes from a manager about our player," Parish stated on his Twitter account.
"So having nicked Victor [Moses] due to administration and then selling for £9m (where I don't recall them being worried about Chelsea getting value for money), Roberto would like it ever so much if we would roll over.
"In the meantime I guess he'll just try to unsettle our player using the papers.
"We didn't reveal any details of their bid we prefer to do these things privately and politely, different rules I guess for 'big' clubs."