"I do think there comes a point where we need to call out this behaviour and go 'enough's enough'. It is draining on Adam ... I just don't know that it reflects well on the game and people have had enough of it."
Swans chairman Andrew Pridham said there was only one word for the treatment of his player.
"If you're booing Adam Goodes I've got bad news for you," he said. "You're a racist. It's not acceptable when the only conclusion you can come to is that there is racism involved in the way the crowds are treating Adam."
The West Coast Eagles condemned the "racist behaviour" of some of its own supporters after Goodes was repeatedly booed and heckled during a game on Sunday.
"It is completely inappropriate and it has to stop," said chief executive Trevor Nisbett.
The heckling included a call to "Get back to the zoo" by a crowd member who was ejected by security but who later insisted he was not racist.
"It was a flippant, off-the-cuff remark and the players would not have heard it for all the booing and banter coming from the crowd," the man said.
The booing on the weekend prompted Lewis Jetta, Goodes' Aboriginal teammate, to deliver an Aboriginal war dance after kicking a goal.
The move, in which Jetta threw an imaginary spear at the crowd, echoed a similar dance by Goodes earlier this year.
Jetta was criticised by some for the "provocative" dance.
"He's a superstar of the game, a superstar for the Swans, fans should show more respect for what he's done for the game," he responded. "All this booing stuff needs to be thrown out the window."
Goodes performed his dance after being subject to constant booing by rival fans - a phenomenon which followed his angry response to a 13-year-old girl who called him an "ape" during a game in 2013.
Goodes - who has twice won the Brownlow Medal, the sport's highest honour - singled the girl out in the crowd but later insisted he did not intend to start a "witch-hunt".
Gerard Whateley, a respected sports commentator, said the booing marked "one of the most shameful episodes in the game's history".
"At its heart here there is a racist element," he told ABC Radio.
"This is disgusting. We are driving Adam Goodes to the end of his career. He'll probably finish at the end of this season and he is going to be booed into retirement."
Francis Leach, a sports commentator, said in The Age: "What a redneck wonderland footy has become."