The 37-year-old actress previously said: "I didn't think I was right for the part, and I know a lot of people will agree, but then again, I don't think Elizabeth Taylor was right for Cleopatra either.
"An artist is colourless, genderless ... It's more complex than just, 'Oh, you chose the Halle Berry look-alike to play a dark, strikingly beautiful, iconic black woman.' The truth is, they chose an artist who was willing to sacrifice herself. We needed to tell her story because she deserves it."
After the trailer was released the official Nina Simone Twitter account, which is now run by her estate, posted: "Please take Nina's name out your mouth. For the rest of your life ... Hopefully people begin to understand this is painful. Gut-wrenching, heartbreaking, nauseating, soul-crushing. It shall pass, but for now... (sic)"
Zoe has not spoken out about the criticism, but her pal insists she "loves the film".
Nina is set to be released in April.