the AFL's Indigenous Round after Goodes kicked three goals and had 30 possessions.
The round is meant to honor Australia's indigenous players' contributions to the AFL. It also comes on the same weekend as national Sorry Day on Sunday, which acknowledges the historical mistreatment of Aboriginal people in the country.
Goodes left the field shaking his head late in the match after pointing to a girl in a Collingwood jumper, and the supporter was led from the venue by security staff. More than 65,000 attended the match.
"To come to the boundary line and to hear a 13-year-old girl call me an ape, and it's not the first time on the footy field I've been referred to as a monkey or an ape - it was shattering," Goodes said Saturday.
He asked those on social media and others not to take issue with the girl, who later apologized.
"She's 13 years old, still so innocent, I don't put any blame on her," Goodes, who has won two AFL titles with the Swans, said.
"Unfortunately it's what she hears and the environment that she's grown up in has made her think that it's OK to call people names."
He said he was convinced the girl would have no idea how calling somebody such a name would make them feel.
"Unfortunately it cut me deep and affected me so much that I couldn't even be on the ground last night to celebrate a victory and to celebrate the Indigenous Round," Goodes said.
Later Saturday, Goodes said the girl had telephoned him to apologize.
"Just received a phone call from a young girl apologizing for her actions. Let's support her please," Goodes tweeted.
AFL chief Andrew Demetriou said the AFL, while disappointed, would not seek any sanctions. And Goodes told police he did not want to press charges against the girl.
"We've got to be very conscious that this is a young girl and from our perspective it's a girl that I think obviously needs to be educated and counseled and we will do our best to be in contact with her parents to offer that support," Demetriou said.
Collingwood president Eddie McGuire went into the Sydney dressing room after the match to offer his apologies for the incident.
"I spoke to Adam, and he told me what he'd heard," McGuire said. "I apologized to him on behalf of the Collingwood Football Club and football people in general.
"We have a zero tolerance at the Collingwood football club on this. It's devastating."
Two incidents of racial abuse were also reported at AFL matches in late April, including one involving North Melbourne's Sudanese-born Majak Daw. Television reports said Daw, who escaped to Australia with his family from civil wars in Sudan, was racially abused by a Hawthorn supporter during a match at the MCG.
Earlier this month, the AFL said some of its top players would be asked to deliver personal appeals to fans to stop verbally abusing players during games, with those pleas potentially being broadcast before each game on scoreboards at all venues.