The 27-year-old, who is married to band Mumford & Sons frontman Marcus Mumford, said he receives the most attention when they venture out together, with his fans usually ignoring her, reported Contactmusic.
"I'm not worried about being a household name. I never get recognised. My husband is recognised all the time. His fans barely look at me," she said.
Carey, who is playing the character of Daisy Buchanan in the big-screen adaptation of Baz Luhrmann's film, insists she has little in common with the role in real life.
"She has shallow characteristics, but she also has a depth of feeling and conviction ... I think she's imprisoned - she's stuck in a marriage for money.