The Boomtown Rats frontman told the audience he had been text messaging with his friend just two weeks prior to her death.
"Many, many times Sinead was full of a terrible loneliness and a terrible despair," he said according to Sky News. "She was a very good friend of mine. We are talking right up to a couple of weeks ago."
"Some of the texts were laden with desperation and despair and sorrow and some were ecstatically happy." he recalled. "She was like that."
"So, we've known that girl most of her life, really. She was a big Rats fan... so, to be honest with you, that's why we're doing very early stuff and we dedicate this gig to her, it's the only thing we can do as musicians."
"We were friends all the way through. She was signed to the same little record label we were signed to, by the same guy, had the same manager and stuff like that so there's a big connection there."
O'Connor died at the age of 56.
No further details have so far been released regarding the Irish singer's death. In a statement to The Irish Times the singer’s family said: "It is with great sadness that we announce the passing of our beloved Sinéad. Her family and friends are devastated and have requested privacy at this very difficult time."
Sinéad released 10 studio albums over her career. Her song Nothing Compares 2 U rocketed to the number one spot worldwide in 1990.