Zaha, who made two friendly appearances for England, committed to playing for Ivory Coast before Southgate's permanent appointment in November.
"It has a lot to do with the less glamorous clubs. The FA don't talk to people that come to Palace games. They talk to people who go to Manchester United and Arsenal games," Parish told The Times.
"He (Zaha) can change a game in a minute. Anybody who watched Wilfried will tell you that some of the things that he does are ludicrous. Do we not want that? I can't believe there was not a role for Wilfried at England."
Zaha has been in fine form for Ivory Coast, scoring two goals in six games.
"The whole England set-up gave Wilfried no love and it is a shame that we lost him. Wilfried was waiting and waiting for that call," Parish added.
"It is devastating for us... We need to capture all the talent we can and give it some love."
Zaha has scored six goals in 27 appearances for 16th-placed Palace who face leaders Chelsea at Stamford Bridge on Saturday.
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
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