Ulster rugby player Nevin Spence, 22, his brother Graham, 30, and their father Noel, 58, died at the family farm near Hillsborough, Co Down last September.
An inquest in Belfast heard the incident was first triggered when Graham Spence entered the tank to find a collie dog that had fallen in.
Emma Rice, who was also overcome by the poisonous gases when she climbed down a ladder to try to find her father and brothers, told Northern Ireland's Senior Coroner John Leckey that she knew how dangerous it was to go into the pit.
"When it comes to the love of your family, it doesn't matter," she said.
After helping to pull her father from the pit, Mrs Rice passed out and fell back into the slurry as she tried to bring Graham to safety.
She was rescued by neighbours. The incident happened at about 6pm on September 15.
Mr Leckey said he was concerned at the number of recent cases he had dealt with involving deaths at slurry pits, saying it was a "very serious problem".
The inquest will conclude today.