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Cam Newton is straight-up apologizing for a comment he made to a female reporter that many branded sexist and belittling ... going so far as to make a video for it.

Cam posted the apology video Thursday evening, saying after careful thought he realized his word choice on Wednesday was degrading and disrespectful to women.

As we reported ... Cam told Carolina beat writer Jourdan Rodrigue that he found it funny a female was asking him about routes after her question about that. He got a TON of backlash since, and even lost his sponsorship with Oikos Greek Yogurt.

In the vid, Cam goes on to say he sincerely apologizes to anyone who was offended ... and that it wasn't his intention to do so.

He even made a plea to young fans of his to be better than him and to do better than him. It's a serving of humble pie at its finest ... but we'll let Cam speak for himself.