Davis, who will be seen in the "Sex and the City" movie later this month, made the remarks about drinking in an interview with the British edition of Shape magazine.
"I was really shy and I didn't know how to come out of my shell," Davis said. "(I drank) for the same reason I loved acting -- I wanted to feel things and express myself and be free. And I'm not naturally that way."
As far as her body image goes, Davis admitted, "I'm a curvy girl."
"I'm never going to be the thinnest person in Hollywood, but the truth is, I don't want to be," she said. "I went through phases when I said, 'I can't have this or I can't have that.' But now I don't deprive myself."
She told Shape the key is eating what you want, but in moderation.
"I never let myself get too hungry. I make sure I eat every three hours or so, mostly protein, good carbs, veggies and salads," she said.