Ulster Rugby star Nevin Spence, 22, his 58-year-old father Noel and 30-year-old brother Graham died in a slurry pit tragedy at the family farm on the Drumlough Road in Hillsborough on Saturday.
"There's been such a lot of expression of goodwill for the family - from as far away as New Zealand," Rev Rodney Stout said.
"All the bereaved are very courageous, very brave. It's a tribute to their Christian faith that has actually given them great hope and stability."
One person survived the tragedy - Nevin's older sister Emma. She was taken to the Royal Victoria Hospital, Belfast, where she was treated for inhalation of fumes. She has since been discharged.
"She still has a little bit of physical recovery to do, but she's very buoyant in her faith and looking to that as a source of strength," Rev Stout added, having spoken to her.
Fondly remembering those who lost their lives, the pastor paid tribute to them as "three incredibly good men" and said it was still hard to take in what had happened.
They've left an incredible epitaph just by how they lived.
Rev Rodney Stout
At Ravenhill, the home of Ulster Rugby, a book of condolence has been opened in memory of Nevin and his family.
The rugby ground will remain open from 9am-5pm every day this week for those wishing to express their sympathy, with many people already adding to the tributes.
First Minister Peter Robinson and deputy First Minister Martin McGuinness have expressed their deep sadness over the tragedy, while former First Minister Ian Paisley was also among those who signed the book of condolence on Monday.
The long-time Free Presbyterian moderator said that he knew the Spence family and added: "It touched me, it really shook me.
"It's a warning to us all - we're not here forever, we're travelling home."
Tánaiste Eamon Gilmore and new Northern Ireland Secretary of State Theresa Villiers both visited Ravenhill to pay their respects.
Meanwhile, at Stormont, MLAs added their expressions of shock and sadness.
DUP Health Minister Edwin Poots, who has known the family for 30 years, fought back tears as he spoke about the losses.
He said the tragedy had thrown the family into grief and stunned friends and neighbours of a family who had farmed their land at Hillsborough for five generations.
Sinn Féin Agriculture Minister Michelle O'Neill said she could only imagine the impact of such a huge tragedy on the Spence family.
She extended her condolences, and raised the need to prioritise farm safety to tackle the dangers faced by those working in the industry.
The three men were very close to each other in life, and that love was expressed in their final moments trying to help one another.
Speakers also recalled the death of Fermanagh Gaelic footballer Brian Óg Maguire in an accident at his workplace in Derrylin.
He died only days before fellow sportsman Nevin Spence lost his life in the farming tragedy.
Nevin was already a star of the Ulster Rugby team and was tipped to have a glittering international career ahead of him.His sporting colleagues have been left shaken by news of the tragedy.
The exact circumstances of the three tragic deaths are not yet known, but the Health and Safety Executive for Northern Ireland is investigating.
A spokesperson said: "HSENI's investigation team is continuing to quickly build up a very detailed picture of events surrounding the tragic accident and can confirm that it is focusing on one particular line of enquiry."
According to Ulster Rugby, a memorial service will be held at Ravenhill on Sunday 23 September at 3pm. More details will be announced in due course.