Writing on social media last night, she said: "Shaney, babba, stick with me. Wherever you may also be, please stick with me. My baby, I don't know how I'm going to live without you."
She also said that Shane "adored" his musician father Donal Lunny.
On Saturday, she announced that Shane, "the very light of my life, decided to end his earthly struggle today and is now with God".
She later said she had formally identified his remains.
Last night, she said: "I would like to thank all care staff at Riverside for the love you gave Shane. You did your best at all times. He loves you for it and so do I. Be at peace."
She also thanked Shane's father, Donal Lunny: "You did your best too, Donal. And Shane adored you. And I will always remember how sweet you have been to him. You have been a lovely father. I am so sorry for your loss."
There has been a huge outpouring of support for Ms O'Connor and her family. Pogues singer Shane MacGowan has said he was praying she can be comforted and find strength following the death of her 17-year-old son.
Writing on social media, MacGowan said: "Sinead you have always been there for me and for so many people, you have been a comfort and a soul who is not afraid to feel the pain of the suffering.
"You have always tried to heal and help. I pray that you can be comforted and find strength, healing and peace in your own sorrow and loss.
"He was a beautiful boy and I loved him. I pray that he can be at peace and also be able to stay connected with you."
Writing on Twitter prior to the discovery of his body, Ms O'Connor, had asked: "How has a 17-year-old traumatised young person who was on suicide watch in Tallaght Hospital's Lynn Ward been able to go missing?"
Announcing his death, she said: "My beautiful son, Nevi'im Nesta Ali Shane O'Connor, the very light of my life, decided to end his earthly struggle today and is now with God.
"May he rest in peace and may no one follow his example. My baby. I love you so much. Please be at peace."
The HSE has said it "cannot comment on individual cases when to do so might reveal information in relation to identifiable individuals, breaching the ethical requirement on us to observe our duty of confidentiality."
If you have been affected by the issues raised in this article, contact the Samaritans on 116 123; Pieta House on 1800 247 247 or text HELLO to 50808, a free 24/7 text support service for people going through a mental health or emotional crisis.