The 62-year-old professional wrestler, born Terry Bollea, broke his silence five weeks after World Wrestling Entertainment fired him over the scandal.
Hogan denied he is a racist, but apologized to fans for the incident.
"I'm not a racist, but I never should have said what I said," he told anchor Amy Robach.
"It was wrong. I'm embarrassed by it. But a lot of people need to realize you inherit things from your environment ... I grew up [in] south Tampa ... the word was just thrown around like it was nothing."
Hogan used racial slurs to describe daughter Brooke Hogan's boyfriend in a sex tape, which was recorded without his knowledge in 2006.
The National Enquirer obtained and published a transcript of the tape last month from Hogan's ongoing lawsuit over the footage.
"Oh my gosh, please forgive me," he later begged.
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"I'm not the Hulk Hogan who rips his shirt off and bang, bang, bang, slams giants. I'm Terry Bollea, I'm just a normal man ... Just because a person makes a mistake, don't throw them away."
Hogan teared up as he spoke of daughter Brooke, who defended him in a heartfelt poem in the wake of the scandal.
The wrestler told Robach he would love a second chance with the WWE, which has stripped all mention of Hogan from the organization's website.
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