The 'A Sorta Fairytale' singer revealed in an interview with USA Today that Cobain's 1994 death had a profound effect on her.
"The night after Kurt Cobain died, I was playing in a church in Berlin. The emotion was palpable. I sang 'Smells Like Teen Spirit'," she remembered.
Amos continued: "The next night, in Ireland, everyone started singing ['Smells Like Teen Spirit'] along just a few bars into it. I was so amazed, I had difficulty finishing the song. But they all carried on for me, singing in perfect reverence of his memory."
Cobain was survived by wife Courtney Love and daughter Frances Bean Cobain.
In September, Amos described her friend and author Neil Gaiman as her "spiritual brother".
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Watch Tori Amos' 'A Sorta Fairytale' music video below: