I don't know what he can say that won't be totally inauthentic. He chose to double down on the kneeling thing at the worst possible time. You can't really walk that back now.
He can't credibly do it alone, but he could do it with teammates at his side and speaking with him. This would be AFTER Brees approaches them, hat in hand, admitting that he doesn't understand and sincerely asking to learn.
Malcolm Jenkins, for instance, is in the building (figuratively). There are thoughtful guys like Demario Davis and Cam Jordan down the hall. I'm sure Ben Watson and Curtis Johnson would take phone calls from Brees.
I doubt that Brees' African-American teammates (past & present) hate him now. I would expect more that they are disappointed in him.