Zaha has joined the Turkish champions on a free transfer after rejecting an offer of a new £200,000-a-week contract to stay at Selhurst Park.
Parish said “after long discussions it became clear” that Zaha “wanted a different challenge” and losing the 30-year-old forward is a major blow to Palace with less than three weeks until the start of the new season.
Palace had been optimistic Zaha would sign a new deal and manager Roy Hodgson admits the club “is losing an iconic figure”. Zaha joined Palace aged eight and made 458 senior appearances for the Eagles, scoring 90 goals.
Parish said: “Wilfried Zaha leaves the club having been our best and most influential player.
“As much as we would have loved him to stay, after long discussions it became clear he wanted a different challenge, to experience something new and somewhere different before the end of his career, and I think that’s something we can all understand.
“I would like to personally thank Wilfried for everything he has done for this football club. He leaves as our most capped academy graduate, our talisman, our greatest player, and he leaves lifelong friends behind.
“He remains a true inspiration for all our young players in the academy and at the early stages of their Palace career — all of whom dream of being the next Zaha.
“We would not be the club we are today without Wilfried. We are entering our 11th consecutive season in the top flight, and he has spearheaded the vast majority of those campaigns.
“A phenomenal player, who gave us incredible moments on the pitch and worked hard in the community helping inspire people off it, he will be treasured in all of our memories. Good luck, Wilfried, I like many Palace fans will watch from afar and wish you every success on your new adventure.”
Hodgson added: “I was really sad to hear that Wilf has decided to leave and start a new chapter in his footballing life. I was always hoping that he would commit his future to the club and I would have the benefit of working with him again this season.”
In an emotional message to Palace fans, Zaha said: “As I start a new chapter I want to speak to you Palace fans who mean so much to me. We have been through so much together.
“There are loads of amazing memories that will stay in my head forever and also some really tough times along the way, but I’m so proud to have played my part in getting us to the Prem and helping to keep us there. I’ve been wearing the Palace shirt since I was eight, it’s literally been my second skin and I always gave everything when I wore it. I have been blessed to play in front of you and call you family from the day you accepted me. From the bottom of my heart, I’m forever grateful.”