The actress told Metro that she also thought she had no chance of winning the role.
Mulligan said: "I thought, 'They'll never let me play that'. I've been in An Education and Never Let Me Go. She's so far removed from anything I've done."
On meeting director Steve McQueen to discuss the role, she added: "Steve kept trying to leave the meeting and I sat him back on his chair and said, 'What do I need to do to get this job?' I told him I felt a passionate desire to play the part."
Mulligan said of playing Sissy: "She was really exciting. Getting to play an extrovert and exhibitionist was a relief."
The star recently admitted that she used to tell people she was a geography student rather than an actress until she was 23.
She also claimed that "there are days when I'm just terrible and I can't act".
> Carey Mulligan: 'An Education role changed my career'
> Carey Mulligan "burst into tears" over 'Great Gatsby' role
Watch Carey Mulligan singing 'New York, New York' in Shame below:
Watch Carey Mulligan talking to Digital Spy about Shame below: