The US singer was performing at the Big Apple as part of her Summer Carnival Tour, when she paid tribute to O'Connor, who passed away last month aged 56.
At her show, Pink described O'Connor as "One of the most brave, outspoken, put-it-all-on-the-line-no-matter-what-happens kind of woman".
"I respected her so much", Pink added, who also revealed that she once used all of her money to make a demo tape of O'Connor's track 'Nothing Compares 2 U', the track which propelled the Irish singer onto the international stage in 1991.
Pink also told the audience, "We used to spend all my money down the Jersey Shore as a kid making a demo tape of this song, so I'm going to sing it". Pink later performed the track as part of a duet with Brandi Carlile.
On the night of O'Connor's death, Pink and Carlile also duetted the song at a concert in Cincinnati, Ohio.
Sinéad O'Connor was found dead at her home in London, with the police and coroner's report finding "no medical cause" for her death. The singer's passing has led to an outpouring of grief from the world of music and beyond.
