Hall of Famer Warren Moon says he truly believes Drew Brees didn't mean any harm with his stance on the national anthem protests ... but now that he's apologized, it's time to step up and put his words to action.

Of course, Brees faced backlash from his teammates and other major sports figures for condemning kneeling during the anthem on Wednesday.

Moon -- who knows the Saints superstar personally -- is giving Brees the benefit of the doubt ... saying the QB was so passionate about his stance, he forgot to take everything into account before speaking.

"I know what type of guy that he is, but I think he just got so wrapped up into his beliefs on the national anthem and the flag that he forgot to open his eyes and listen to what was being said by others that might not have his same belief about what all that means to them," Moon tells TMZ Sports.

Brees apologized in a lengthy statement and video and vowed to be a leader for the black community ... and Moon says the next step in getting forgiveness is proving he's genuine.

"I don't know if the apology is going to be enough, but at least it's a start."

"I think he has to maybe now get out there and try and do some things physically to show that he's putting his money where his mouth is and maybe get on camera to talk about those things so people can look in him in the face, look him in the eye and see if he's sincere or not."

(A short time after we shot our interview with Warren, Brees posted an video apology.)

Moon says Brees isn't the enemy people are making him out to be ... but can use this as an opportunity to hear from others with different experiences.