Contostavlos admitted during the interview that she suffered "a bit of a nervous breakdown" following the online leak of the video, which featured her performing a sex act on former boyfriend Justin Edwards.
The 23-year-old X Factor judge and N-Dubz popstar played down the actual content of the video, arguing that it couldn't technically be considered a sex tape.
"Number one, there was no sex involved," she told Carr.
"Number two, a 19-year-old who's just starting to learn and her boyfriend pulls out a camera, doesn't really class as a sex tape.
"Everyone does it. Such a big deal has been made out of it that I feel like a bloody alien."
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Contostavlos said that she was surprised by the positive public reaction to the incident, confessing that she originally feared people would brand her "a slapper".
"I have been surprised by how nice everyone has been," she said. "I haven't done anything wrong, so any normal person would be like, 'She's human'."
She added: "I'm feeling depressed and of course I'm gonna have a bit of a nervous breakdown. But I sat there, did my crying and I haven't jumped off a building yet."
Contostavlos also confirmed rumours that she is dating former Skins actor Jack O'Connell and insisted the sex tape incident hadn't put her off men.
"I'm not gonna judge someone on someone else's actions," she said.