Robert Christie died on 7 June 2014 after the accident on a family friend's farm on Ballynaloob Road in Dunloy.
His father, Robert Christie senior, was left critically ill but made a partial recovery.
The coroner extended her deepest sympathy to the child's parents.
She said the death had again brought to the fore the risks arising with slurry tanks.
"I hope by highlighting this tragedy no other family will have to endure what they have had to go through with the death of poor Robert," the coroner said.
Robert Christie Snr told the inquest he and his son, who was known as Bob, had gone to crush grain at a neighbour's farm that Saturday morning.
The farmer, Robert Brownlow had asked Mr Christie if he would assist him with attaching the slurry pump in the shed.
Mr Brownlow said this was a normal procedure but that due to his age and health he was no longer "able to do it myself".
"I knew there was a danger, but there had been no problems doing it in the past," he said.
Mr Christie said he lifted the covers in the shed and reversed the tractor in.
"I attached the pump and saw Bob had got into the tractor cabin with me," he said.
"With the tractor straddling the two slats I turned on the pump and sadly that was my last memory of that day."
The father and son were found collapsed on the floor of the shed about four feet apart about 30 minutes later by Mr Brownlow who called for help.
A postman who was in the area at the time moved Bob from the shed into the house.
Despite extensive efforts by neighbours and emergency services he showed no signs of life.
He was airlifted to hospital in Belfast but medical staff were unable to resuscitate him.
In his report, David Lowe from the Health and Safety Executive said it was likely that both father and son lost consciousness at speed.
He told the inquest that he believed Mr Christie, in seeing his son in difficulty, went in closer to the tank to help.
"Precautions must be followed when dealing with slurry and in this case many of them were, Mr Lowe said.
"The slurry tank was particularly full and the initial stages of agitation (where the gases are mixed) the gases are the most potent."
The HSENI guidelines recommend that once the pump is started you remain out of the area for at least 30 minutes.
"Also there was very little movement in the air that day which left limited ventilation and led to this catastrophe," Mr Lowe added.
An inquest into the death of an eight-year-old boy has found that he died from asphyxia from the toxic gases released during the mixing of slurry at a farm in County Antrim.