The star forward posed for a selfie with a Fremantle fan ahead of Sunday's match at Optus Stadium, which later appeared on his Instagram account with his comment, "I have time for everyone".
After the Crows' upset loss, he posted another image of the comments below the picture which included "Why with a monkey" by an unnamed user, to which he replied, "I have no time for this".
The Crows believe the comment was made by a Perth-based fan.
"It's unacceptable that our Indigenous members continue to be racially vilified over the fence during games, in the community and in this instance, on social media," AFLPA chief executive Paul Marsh said via a statement released on Tuesday night.
"Despite the outstanding leadership Indigenous players continue to display both on and off the field, they still remain targets for such shameful behaviour.
"This most recent incident involving Eddie Betts provides another opportunity to educate people about the significant hurt these types of words can cause a player, his or her family and their community."
Betts was the target of racist abuse in 2016 when a Port Adelaide fan threw a banana onto the field during a showdown clash at Adelaide Oval.
While clearly saddened and disappointed by the supporter's actions, Betts forgave her and hoped the incident would help stamp out racist behaviour.
Crows Indigenous liaison officer Jeremy Johncock condemned the latest racist slur against Betts.
"Our entire club is committed to continuing to educate the broader community to promote a deeper respect and understanding of Aboriginal and Torres Strait Islander cultures and stamp out racial behaviour," Johncock said.
"If this means we need to educate one person at a time so be it. For our Aboriginal and Torres Strait Islander players, in particular, any form of racist behaviour is extremely damaging and hurtful to them, their families and communities."