The show has long been criticised for how it represented the character, who was regularly mentioned throughout the series before Kathleen Turner took on the role for two guest appearances in season seven.
During an interview with The Conversation on the BBC World Service, Marta, who co-created the show with David Crane, said: “We kept referring to her [Chandler’s transgender parent] as ‘Chandler’s father’, even though Chandler’s father was trans.
“Pronouns were not yet something that I understood. So we didn’t refer to that character as ‘she’. That was a mistake.”
Marta, who is also the creator of Netflix hit Grace And Frankie, said she now strives to create inclusive and diverse workplaces.
“I like very much to create an environment where we have a happy set and a happy crew,” she said.
“It’s very important to me that where we are is a safe place, a tolerant place, where there’s no yelling.
“I fired a guy on the spot for making a joke about a trans cameraperson. That just can’t happen.”
In an interview on Watch What Happens Live, Kathleen said: “Of course, I wouldn’t do it [today] because there would be real people able to do [the part],” she explained.
Kathleen also said she was attracted to the role because she felt she would be a “woman playing a man playing a woman”, joking: “I [hadn’t] done that before.”
Meanwhile, Marta reiterated her regret at Friends’ lack of diversity, having cast a group of six white actors in the show’s main roles.
She recently pledged $4 million (£3.3m) to fund an endowed chair at Brandeis University’s African and African American studies department after “admitting and accepting guilt” over the sitcom’s casting.
Marta told BBC World Service presenter Kim Chakanetsa: “Friends has been criticised in a number of ways. The biggest one being that we did not have enough representation of Black people.
“And over the course of the last few years I’ve gotten to the point where I can say unfortunately yes, I am guilty of that. And I’ll never make that mistake again.
“I was clearly part of systemic racism in our business. I was unaware of that, which makes me feel stupid. That was a very valid, extremely difficult criticism which still… I get emotional about.”
She added: “If I knew then what I know now, there are certain things I would have changed. But I didn’t know them and I have since learned.”
The full interview with Marta Kauffman on The Conversation will air on BBC World Service on 11 July at 11.30am.