The former Eurythmics frontwoman's cover of Nothing Compares 2 U was a stand-out moment during the Grammys ceremony.
The Nothing Compares 2 U singer died last year, at the age of 56.
The two singers had a public disagreement after Miley released her divisive Wrecking Ball music video a decade ago.
Fans of the Irish singer lined the streets of her former hometown to say goodbye following her private funeral.
"You praise her now ONLY because it is too late," Morrissey wrote of the Irish singer, whose death was announced on Wednesday.
Pink also credited Sinéad – who died on Wednesday at age 56 – with blazing a trail for her own unconventional journey as a musician.
Showbiz luminaries including Ice-T and Bryan Adams joined Ireland's prime minister and others in paying their respects to the Nothing Compares 2 U singer.
Sinéad O’Connor Thought Tearing Up The Pope's Picture Defined Her Career In A 'Beautiful F***ing Way'
People are sharing the Irish singer's reflections on her most controversial moment in the aftermath of her death.
The 1990 hit single Nothing Compares 2 U made the Irish singer an international star.
The singer wrote on Twitter: "You will always be my light. We will always be together. No boundary can separate us."