She said: "When it comes to stuff like 'X-Men, I just didn't think that I would get that part.
"I just think I auditioned because people were auditioning and my agent was like, 'Please go', and had to talk me into going."
However, the young star explained her parents have warned her not to get too caught up in the trappings of the film industry, and they have helped to keep her "level-headed".
Zoe added: "Having well-known parents is kind of a double-edged sword. It's given me wonderful opportunities, but people also like to knock you down because of it too and say that you have got things because of that.
"They told me not to take it seriously. People get very serious about the Hollywood fame thing and the reason I think I came out level-headed was that they didn't raise me to think it was anything serious. I had no illusions. People get way too deep about it and in the end it's just a job and we're all equal."