Warnock is renowned for his straight-talking approach to management, with Parish keen to outline that the duo have an excellent relationship as a result of his no-nonsense attitude.
However, Parish does think the Palace boss needs to learn to bite his tongue if he feels he has been on the receiving end of wrong decisions from match officials, having been handed a £9,000 fine earlier this month for claiming that Craig Pawson was "influenced" during his side's Premier League defeat against Chelsea.
Warnock has since admitted that he will have to "watch what I say" to avoid sanction in future, and Parish agrees.
"I don't think Neil should complain about referees," Parish told the London Evening Standard. "I've told him that.
"I don't think it helps us with matches.
"I don't think a manager should do anything other than try to help his club."
Despite publicly questioning Warnock's outspoken approach, Parish insists he is more than happy with the progress being made during the 65-year-old's second spell in charge.
Palace beat Liverpool 3-1 on Sunday to haul themselves out of the bottom three and the club's co-owner is setting his sights high.
He added: "Neil's brilliant.
"From a communications point of view, he's the easiest manager I've ever had to chat to.
"There's no reason why Palace can't cement itself as a Europa League challenging club.
"The Champions League is really difficult for any club outside the top four or five.
"You might get the odd wild card. The next level down - right down to ninth - is very flat now. "
