Quaynor was the target of a homophobic slur from Adelaide's Izak Rankine in an August 16 game last year that resulted in a four-game ban for the star Crow.
Yet the Magpie defender was booed by sections of the Adelaide Oval crowd during Collingwood's 34-point win on Thursday night.
"We ... strongly believe there is a line between passionate support and behaviour that falls short of our values and those of the game," Crows chief Tim Silvers said in a statement on Friday.
"The behaviour of some crossed the line last night.
"Put simply, it was inappropriate and not good enough.
"Respect for all players, coaches, officials and fellow supporters is paramount, and it is a standard we must all uphold."
Post-match, Collingwood coach Craig McRae said it was "fascinating" why sections of the Adelaide Oval crowd booed Quaynor.
And his Crows counterpart Matthew Nicks said it was "not ideal" that the Magpie defender was again jeered by spectators.
"It's a fascinating narrative around why they would boo him," McRae said after his side's 16.12 (108) to 11.8 (74) triumph.
"My understanding is he was a victim of a homophobic slur - and he's getting booed for that.
"It's a fascinating world we live in."
McRae sought out Adelaide's Rankine after the final siren.
"I said: 'Mate, we've got great respect for you'," the coach said.
"People are allowed to make mistakes; they are, we're all human. I've got great respect for him. He's a sensational player.
"And I don't know him as a person, but the way he stood up... took it on the shoulders or whatever, however you want to put it, there's something to be said about that.
"That's life, isn't it: make a mistake, fix it, or get on with it and improve yourself."
McRae's 10-year-old daughter Charlie was in the Adelaide Oval media room as the coach commented.
"I teach her: we don't boo, that's all I can control," he said.
"People pay their money and they do what they like when they come to a game.
"I teach my children that we don't boo. We show respect to all people."
Crows boss Nicks, on the eve of the match, called for supporters to be respectful in what was Rankine's first game against the Magpies since his suspension.
"I mentioned it during the week about why we play footy, why people come to the footy," Nicks said post-match.
"It's about entertainment, it's about enjoyment, passion. The game is a passionate game and sometimes we lose our way in that a little.
"It's not ideal, the way it played out tonight."
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