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The Gilded Age star, 55, opened up about the decision in an interview with Entertainment Tonight published on Thursday.
"I think we were very lucky that those changes were able to be made," said Nixon. "And I think we are very proud of our show."
Noth's return to the Sex and the City revival was short-lived as his character, John James "Mr. Big" Preston, died in the premiere episode. TV Line recently reported that Noth, 67, was set to return for a brief cameo alongside Sarah Jessica Parker in the first season's final episode. The two were previously spotted filming scenes in Paris.
TV Line reported that the footage will now "not make it to air."
Shortly after the premiere episode aired last month, two women accused Noth of sexual assault in a report by The Hollywood Reporter. The accusers shared similar accounts of how he allegedly assaulted them, but Noth — who has been married to Tara Wilson since 2012 — denied the allegations and claimed that the interactions were "consensual."
"The accusations against me made by individuals I met years, even decades, ago are categorically false," a previous statement from Noth read. "These stories could've been from 30 years ago or 30 days ago — no always means no — that is a line I did not cross. It's difficult not to question the timing of these stories coming out. I don't know for certain why they are surfacing now, but I do know this: I did not assault these women."
Noth then denied allegations from a third woman who accused him of rape in a Daily Beast report. At the time, his rep claimed "the story is a complete fabrication" and "read like a piece of bad fiction."
When singer Lisa Gentile came forward with her allegations against Noth, she claimed the actor said he'd "ruin" her career if she "ever told a soul about what happened." At the time, Noth's rep did not immediately respond to PEOPLE's request for comment on the matter.
The allegations resulted in Noth's Peloton advertisement being immediately pulled. Not only did Noth also reportedly lose a $12 million deal to sell his tequila brand, Ambhar, but Universal Television and CBS additionally confirmed that he "will no longer film additional episodes of The Equalizer, effective immediately."
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Nixon, Parker, 56, and Kristin Davis spoke out in a previous joint statement.
"We are deeply saddened to hear the allegations against Chris Noth," the statement read. "We support the women who have come forward and shared their painful experiences. We know it must be a very difficult thing to do and we commend them for it."
If you or someone you know has been sexually assaulted, please contact the National Sexual Assault Hotline at 1-800-656-HOPE (4673) or go to rainn.org.