"There were a lot of positive comments surrounding Donovan's post," Snyder said, according to ESPN's Tim MacMahon. "That said, there were also some comments that were abominable and things that we all should never tolerate."
Mitchell shared an Instagram post on June 19 in commemoration of the end of slavery in the U.S. It read "Free-ish since 1865."
Subsequent abusive comments on the post led the star guard to respond on Twitter.
"Can't see how y'all can openly cheer for us then when it comes to this be against us so openly," the 23-year-old wrote.
Snyder said the negative reaction is proof that society has a ways to go.
"To the extent you can rationalize some of those negative comments by saying there were positive comments, I think that's a mistake," the coach said. "We all have to be that diligent, because as long as those comments are there, there's work to be done."
He added: "The road from complacency to complicity is a slippery slope. I think as we educate ourselves more and more, that complacency falls off and then it's an opportunity to act."
Snyder is a member of the National Basketball Coaches Association's committee on racial injustice and reform, which was formed in May in the wake of the killing of George Floyd in police custody.