Morgan Barnard, 17, Lauren Bullock, 17, and Connor Currie, 16, died following a crush near the entrance to a hotel in Cookstown on St Patrick's Day.
Schoolchildren formed tearful guards of honour during back-to-back funerals attended by thousands of friends and relatives on Friday.
Archbishop Eamon Martin told mourners: "Words fail us at times like this. All that really matters, and makes a difference, is love and friendship and compassion.
"And only faith can dare to speak into the darkness of these days to offer a glimmer of light and hope in this valley of tears."
Hundreds of young people had just arrived on buses and were waiting outside the Greenvale Hotel to get into the popular nightspot.
Police said some fell and were trodden underfoot.
Hotel owner Michael McElhatton, 52, was arrested earlier in the week on suspicion of manslaughter and bailed to return for future questioning.
A 40-year-old man who was also arrested on suspicion of manslaughter has been released on police bail pending further inquiries.
Fr David Moore reflected at one of the funerals: "St Patrick's Day 2019 will be called to mind as the awful day when three beautiful young people, all in the prime of their lives, were overpowered, literally in the mad rush of our modern world and needlessly lost their lives.
"On Sunday night, and during the early hours of Monday, a dark and threatening cloud hung over all of us, as we struggled to understand and come to terms with the tragic turn of events on what ought to have been a night of fun, dance, friendship and laughter."
Morgan's humour brightened people's lives, funeral-goers heard.
One friend said: "Morgan was my best friend and no matter where he is he will always be my best friend.
"And I am going to love him forever."
Fr Aidan McCann at St Patrick's Church in Dungannon added: "He was a vivacious, charismatic and energetic young man who nobody had a bad word to say about."
In Donaghmore, a village a few miles from Dungannon, Lauren's funeral was held.
Her pink and white coffin was decorated with paintings of flowers.
Fr Moore said: "Lauren was a girl who loved to get dressed up, loved make-up, her nails done, a bit of style, her hair just right."
Lauren's friends described her as having a "warm and bubbly personality with a very infectious smile", the priest said.
Her passion was cheer-leading, and team-mates from the Euphoria All Star group cut a purple streak of colour amid the drab occasion.
Others wore purple ribbons in their lapels.
A funeral pamphlet had a photograph of Lauren with her dog Benji on the front, her "pride and joy".
The priest added: "Lauren has had too short a time on this earth, but for her 17 years of life she has certainly achieved a lot, she used her time well and wisely."
Connor was remembered by more than 1,000 at nearby St Malachy's Church in the village of Edendork as a "courteous and appreciative" student who wanted to become an accountant.
Former teammates at Edendork Gaelic Athletic Association (GAA) football club formed a tight circle around his coffin in a final tribute.
His mother Ciara and father Eamon described him as a "gem".
Fr Kevin Donaghy said: "And a winner indeed he was: a winner of a loving family; a winner of many loyal friends and team-mates; a winner in school life and on the sports field - and a winner above all, of a place among the ranks of God's children."
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