Incognito is alleged to have sent a voice mail message to Martin in April referring to the offensive tackle as a "half nigger piece of shit", as well as threatening to "kill" him.
The 30-year-old acknowledged that he was wrong to use such offensive terms, but insists that the language used in the locker room is not representative of him as a person.
"I'm not a racist, and to judge me by that one word is wrong. In no way, shape or form is it ever acceptable for me to use that word, even if it's friend-to-friend on a voice mail," Incognito told Fox Sports.
"It's thrown around a lot. It's a word that I've heard Jon use a lot. It's not saying it's right that I did it and used it in a voice mail.
"But it's a lot of colourful words that are being thrown around in a locker room that we don't use in everyday life."
Incognito also claimed that Martin had left him similar messages, and that such exchanges were simply the nature of their relationship.