Smith, who plays Elle Woods in the West End musical, told The Times that she never expected to get the part.
"I usually play slappers and chavs," she joked. "But this is a real monster of a part. There's singing, dancing, comedy, pathos... I'm scared I'm out of my depth."
Speaking about her audition, she continued: "I love musical theatre, but I haven't got a soprano voice like all these gorgeous women who can sing. I didn't actually believe I could get the part, and I lost my bottle a bit. The director kept saying, 'Breathe!', because my legs were shaking and it looked like I was going to pass out.
"But I got it together, and they called me 20 minutes after I left the room and said I'd got it. I was gobsmacked - there must be a million girls who could have done the part better than me."
Smith added that she can relate to Elle, who attends law school in an attempt to win back her boyfriend.
"She is that naive, vulnerable girl," she explained. "Everyone looks down their nose at her and she steps up. So yeah, I'd like to think I am doing that.
"The thing I'm finding difficult is that she's so rich. That's so not me - in fact, I keep forgetting to cross my legs all the time. All these long gorgeous locks and pink dresses and they're going, 'Sheridan, you're sitting like a boy'."
Legally Blonde: The Musical is currently in preview and opens officially at the Savoy Theatre on January 13.