She goes on defiantly: 'I tried to be a good girl, I tried to be the perfect wife. Diminished myself, and I swallowed my light.
'I tried to become all that you expect of me. And if I was a failure, I don't give a ****.'
Another new song, 'Bang Bang', is not so obviously autobiographical but finds the star in a murderous mood over a former lover.
'Bang bang, shot you dead, shot my lover in the head,' she sings.
'And if I see that bitch in hell, I'm gonna shoot him in the head again, cuz I want to see him die, over and over.'
The feisty lyrics, revealed in a private performance in New York on Friday, are the latest in a series of barbed comments from both sides.
It is not the first time the 53-year-old singer has spoken about her split from the British film director - but it is her first song about it.
In January, she told Newsweek magazine that her marriage, which ended in 2008, was initially "flawless" but she had started to notice "cracks in the veneer" as time went by.
She added: "You think: 'This isn't what I thought it was going to be' and 'How much am I willing to sacrifice?'"
The couple had a son, Rocco, 11, and adopted another boy, six-year-old David Banda.
Ritchie, whose films include the latest Sherlock Holmes adaptations, has also spoken about the split.
He told US magazine Details last year that, while he does not regret his time with Madonna, the drama was often too much for him.
He added: 'I stepped into a soap opera and I lived in it for quite a long period of my life.'
While he admitted his connection with Madonna made him rich, he said in the process he "stumbled into all sorts of hollow victories".
Friends of his have also claimed the singer's strict diet, Kabbalah religion and obsession with yoga made her hard to live with.
Madonna's two marriages - to Ritchie and previously to actor Sean Penn - both ended in divorce and she has said she will never marry again.
But there are reports that she is considering a proposal from Brahim Zaibat, her 24-year-old French dancer boyfriend.
She admitted in January that she missed some aspects of marriage. "I don't want to live on my own ... I need apartner in my life and I think most people feel that way," she said.
- Daily Mail