The TV presenter appeared in her first interview since the incident on Real Time with Bill Maher, in which the pair complained about “woke language”.
“I’ve been called so many things in my life, I am so used to being called names, but a racist is one I will not take,” Osbourne said.
“I’m going to be just fine, I’m fine, as I said I’m a fighter, I’m fine.”
She added: “It’s not fair, because it isn’t about being a racist. “It’s about maybe about not knowing what is correct and woke for your language that day, because it changes from day to day.”
Maher threw in: “The idea in there is that you have two choices if you are white, you are either a racist or a racist and you don’t know it.”
Maher issued an apology in 2017 for dropping the N-word on live TV during an interview with Nebraska senator Ben Sasse.
Osbourne left The Talk in March after a heated debate with her former co-host Sheryl Underwood.
During the incident, Osbourne had defended her friend and fellow broadcaster Piers Morgan over his controversial criticism of a high-profile TV interview given by Meghan Markle, the Duchess of Sussex, and her husband, Prince Harry, with Oprah Winfrey.
This led to a clash with Underwood, who said Osbourne was giving “validation” to “racist views” in her support of Morgan.
Osbourne reacted strongly to the suggestion, claiming she felt like she was “about to be put in the electric chair”, as she clutched a tissue and told Underwood: “And don’t you try and cry, because if anyone should be crying, it should be me.”
Broadcaster CBS later said Osbourne’s behaviour towards Underwood “did not align with our values for a respectful workplace”.