The AFL chief executive officer spoke following a media conference by Goodes on Saturday morning, in which Goodes expressed his hurt at the slur directed at him by a 13-year-old female spectator.
The girl has since contacted Goodes to apologise for her comment, which was captured during television coverage of the game.
"This one-off incident involving a thoughtless, ignorant and incredibly hurtful comment from a spectator was obviously disappointing, particularly at the start of the AFL's Indigenous Round," Demetriou said.
"Discrimination and vilification in any form has no place in our game and Adam Goodes has again demonstrated his leadership qualities by standing up to it. He is a wonderful ambassador for our game and an inspiring leader for the Indigenous community.
"At the same time, the AFL community immediately rallied behind him in an extraordinary but not surprising display of support and solidarity.
"In particular I want to single out the immediate and emphatic response from Collingwood Football Club president Eddie McGuire and his club, who last night extended an apology and expressed support for Adam.
The incident was a sour start to Indigenous Round, and Demetriou called on fans to be vigilant to stamp out racism.
"Throughout this week we have saluted Nicky Winmar's iconic gesture of pride 20 years ago and last night demonstrated that racial vilification is not only unacceptable but will not be tolerated in our game - on both sides of the fence.
"It was also a reminder that we must remain vigilant and continue our efforts to raise awareness about the hurt and damage that is caused by vilification."
Demetriou extended AFL support towards the girl.
"The AFL stands ready to provide help, education and appropriate counselling to her and we invite her parents to make contact with us to allow for this to happen in a confidential setting."
Demetriou said that the remainder of Indigenous Round took on added meaning following the incident.
"Indigenous Round is a wonderful opportunity to celebrate the extraordinary contribution made to our game over many years by Indigenous Australians and the overwhelming response to this isolated incident reaffirms that commitment.
"We all have a role to play in stamping out ignorance and vilification, and I urge all parents to speak with their children about the lessons that emerge from this regrettable matter."
