The 80-year-old was heard in a recording released by TMZ telling his girlfriend V Stiviano that he did not want her to bring black people to games at the Staples Center.
He has been fined $2.5m (£1.5m) for his comments, which is the maximum financial penalty that the league can impose.
"I'm a good member who made a mistake and I'm apologizing and I'm asking for forgiveness," he told CNN.
"Am I entitled to one mistake, am I after 35 years? I mean, I love my league, I love my partners. Am I entitled to one mistake? It's a terrible mistake, and I'll never do it again."
Sterling has reportedly said that he will not sell the Clippers despite his ban.