Nicole Scherzinger The Backstage Cry Sesh -- Caught on Tape

12/9/2011 1:15 PM PST

Nicole Scherzinger: The Backstage Cry Sesh ... Caught On Tape! [Video]

"X-Factor" judge Nicole Scherzinger claimed she "died inside" when she saw the look on Rachel Crow's face last night ... after the 13-year-old was eliminated -- and TMZ has obtained footage of the emotional backstage meltdown.

Nicole told producers after the show, half in denial -- "I couldn't make that decision on my own ... I didn't send her home. I adore Rachel."

Between tears, Nicole added, "When I saw Rachel's look on her face, I just died inside."