The 33-year-old Sydney Swans player, who is of Indigenous Australian heritage, was called an "ape" by the 13-year-old spectator at Friday's AFL game against Collingwood at the MCG in Melbourne.
Goodes told a news conference he was "gutted" by the remark but added that the girl, who was escorted out of the stadium following the incident, had called him to apologise.
Victorian premier Denis Napthine said he was disgusted by the incident which he termed as "totally unacceptable".
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"I am going to be contacting the AFL and asking if they would like to work with the Victorian education department to see if we can institute improved programmes across our schools to make sure all young Victorians understand that this sort of abuse based on racism, culture, is totally and utterly unacceptable in modern society," Napthine told reporters.
Goodes admitted he was too distraught to celebrate his team's 47-point win over Collingwood but refused to hold the girl responsible.
"I'm pretty gutted to be honest," he told reporters.
"You come to the boundary line to hear a 13-year-old girl call me an ape... it was shattering.
"It's not her fault, she's 13, still so innocent. I don't want to put any blame on her. Unfortunately it's what she hears and the environment that she's grown up in that has made her think that it's OK to call people names.
"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," Goode, who has won the AFL's prestigious Brownlow Medal for fairness on two occasions, added.
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