Lauren Bullock, 17, Morgan Barnard, 17, and 16-year-old Connor Currie, from Dungannon in Co Tyrone, died in the tragedy at the Greenvale Hotel.
Archbishop Eamon Martin said the joy and celebration of Saint Patrick's Day in the Archdiocese of Armagh "has given way to shock and sadness".
"Our heartfelt thoughts and prayers are with the families and friends of Lauren, Connor and Morgan, and with all of those who were caught up in the horror and distress of what happened, including those injured and traumatised, and the emergency services and staff who responded."
Police said it appeared that people had fallen and then been fatally injured, but are still investigating the cause.
Up to 400 people were in the queue or in the car park at the time and police investigating the deaths have said there could have easily been more deaths.
Archbishop Eamon highlighted how difficult it would be for the victims' loved ones to come to terms with what happened.
He added: "The sudden loss of any life makes us stop in our tracks and ask, 'Why?' - but when the lives of three young people are taken away so abruptly, and in the fullness of their youth and potential, we are left speechless and the grief is overwhelming.
"Words are inadequate at times like this: only compassion, love and faith can offer consolation to their loved ones and a glimpse of hope in the resurrection of Christ."
Books of condolence were opened on Tuesday morning at The Burnavon Arts Centre in Cookstown, at Ranfurly House, Dungannon, and at The Bridewell centre in Magherafelt.
The hotel can take up to 500 people and attracts people from across the country.
Owner Michael McElhatton gave CPR to the victims.
He said: "We are all deeply shocked and saddened by the traumatic events of last night.
"We offer our heartfelt sympathies to the families and friends of the three young people who have lost their lives."
A 16-year-old girl is in a stable condition in hospital, while another two teenagers were treated for injuries.
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