The former player on Thursday posted the home security footage to social media, showing a white car driving by as the children played.
A male is heard repeatedly shouting a racial slur as the car goes by, before the children leave the court.
View this post on Instagram A post shared by Eddie Betts (@eddiebthe3rd)
"Aboriginal kids deserve to be able to play safely, free from racism and abuse over the fence," Betts wrote on Instagram.
"We are not even safe in our own homes.
"If you know who this is please let me them know that I'm open to having a chat about how much this hurts our kids."
The post drew messages of support for the AFL great and horrified reactions, with the Western Bulldogs commenting: "Disgraceful. Sending love Eddie."
Western Bulldogs coach Luke Beveridge further addressed the incident at his weekly press conference on Friday morning, saying the attack made him angry and emotional.
"Obviously, as a club ... everyone has put something out there to express their support and love and concern for the Betts family," Beveridge said.
"Quite simply, it just makes my blood boil.
"Everyone feels the same. I hope everyone does."
Victorian Premier Jacinta Allan condemned the incident and offered her support to Betts' family.
"It is sickening and disgusting that kids playing basketball in their own backyard have to be subject to such disgusting racial abuse," she said.
"He has talked a lot about his own personal experience with racism and he has been a strong and proud Indigenous man."
The AFL Players' Association also offered support, calling the incident awful.
"No-one should ever have to experience this. We stand with you Eddie," the group wrote.
Federal MP for Higgins, in Melbourne's southeast, Michelle Ananda-Rajah said she had experienced similar situations.
"As a person of colour, I have dealt with this too," she said.
"Now I stare down the haters. The children belong here, they make our community more vibrant and stronger.
"They should not fear being here."
Melbourne player Christian Petracca was also among commenters calling the racial attack disgusting.
Betts retired from the AFL in 2021 after 350 games with Carlton and Adelaide.
Eddie Betts retired from the AFL in 2021 but cited the AFL environment as unsafe because of racism. (Scott Barbour/AAP PHOTOS)
He was repeatedly subjected to racist abuse online throughout his career and had a banana thrown at him during a match at Adelaide Oval in 2016.
At his retirement announcement, Betts said he was tired of fighting racism and declared the AFL was not a safe environment for Indigenous players.
Now 37, Betts has spoken publicly many times about the abuse thrown at him and has previously implored Australians to help tackle racism.
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