Ulster Rugby player Nevin Spence, his 58-year-old father Noel and 30-year-old brother Graham died in a slurry pit tragedy on the Drumlough Road property on Saturday.
The exact circumstances of their deaths are not yet known, but it is believed Mr Spence was the first to become trapped in the pit, and his eldest son Graham - a father-of-two - went to help him.
When he got into difficulties, Nevin, 22, and his sister Emma went to their aid.
Emma, a well known artist, was taken to Belfast's Royal Victoria Hospital for treatment for the inhalation of fumes. Her condition is described as stable.
The Spence family are trying very hard to come to terms with their tragic loss. The three men were very close to each other in life, and that love was expressed in their final moments trying to help each other.
Emergency services went to the family farm shortly after 6pm on Saturday following reports that four people had fallen into the slurry pit.
The Ambulance Service's John McPoland said the fumes emitted by slurry can cause people to lose consciousness very quickly.
"When anyone goes in to rescue them, as the Fire and Rescue Service did last night, they have to make sure they're well protected, and the Fire and Rescue Service performed really well last night with their breathing apparatus in recovering the people as quickly as they possibly could, but unfortunately the outcome was not the positive one that we would have liked," he said.
A spokesman from the Health and Safety Executive for Northern Ireland (HSENI) said: "From HSENI's initial investigations, it understands that the three family members who entered an underground slurry tank died from the effects of exposure to slurry gases."
The HSENI confirmed two of its senior inspectors were at the Spence family farm on Saturday evening and have begun an investigation into the circumstances of the deaths.
"The exact sequence of events is not yet clear but HSENI is investigating a definite line of inquiry," said a spokesman.
Ulster Farmers' Union President Harry Sinclair said farming families across Northern Ireland were shocked by the tragedy.
"Our industry is based on family farms and a lot of families are sitting this morning thinking, 'it could have been anyone of us' and it's brought home to so many of us that in the circumstances it could have been any of us," he told UTV.
I know we've had a lot of farm accidents over the last 18-20 months but whenever you get three members of one family and another one ill, it's just unbelievable.
First Minister Peter Robinson and deputy First Minister Martin McGuinness also expressed their sympathy for the Spence family.
"This tragedy has shocked the entire community and is a terrible reminder to us all of the dangers of farming life. Our thoughts are also with farmers everywhere at this time," they said in a statement.
"Nevin was a rising star of local rugby... His untimely death is a blow for the game in the province and we sympathise with his teammates and everyone at Ulster Rugby who have lost a true colleague and friend," they added.
Agriculture Minister Michelle O'Neill also gave her condolences to the Spence family.
"I am shocked and deeply saddened to learn of this terrible tragedy which has hit this hard working farming family.
"My thoughts and prayers are with Noel, Graham and Nevin and their family and friends at this extremely difficult time.
"I also hope and pray that Emma Spence who was also involved in this accident makes a full recovery," said Minister O'Neill.
Secretary of State Theresa Villiers said her thoughts and prayers are with the family.
"I am deeply saddened by this tragedy. It will be devastating for the family and friends of those who have lost their lives and a cause of great sadness for the whole community. This loss will be particularly strongly felt across farming and sporting circles," she commented.