Darren Sykes, 44, set fire to his home in Penistone, South Yorkshire after luring Jack, 12, and brother Paul, nine, there with new a train set.
Sheffield Coroner's Court heard Jack, who later died, told doctors and police his father had set the house on fire.
Both boys were unlawfully killed, coroner Christopher Dorries ruled.
Mr Sykes, who had been divorced for two weeks at the time of the fire, was caught on CCTV buying petrol in portable containers from a filling station near his home in Tennyson Close on the day of the blaze.
He died in the fire on October 22 along with Paul.
Monday's inquest into his death recorded a verdict of suicide.
Before his death, Jack was heard to say "he did it" to doctors and police, the inquest heard.
Claire Sykes, the boys' mum, told the court she still carries guilt for what happened.
She wished she had been home earlier from work, she said, and been able to stop Jack and Paul from going to see their father.
"I wasn't there when they really needed me as a mum," she added outside court.
"The only thing I could do was hold them in my arms when they died."
Andre Spencer, Mr Sykes' former boss, said he was one of a number of people to get a text from his employee just moments before the fire started.
"To be honest, I thought he was being a bit dramatic and that he would be at work the following day," he said.
"It was only when I got a phone call from another person who received the same message that we decided to contact the police.
"He was very depressed. He thought that he was going to lose access to his children."
Barnsley Council said it had begun a serious case review into the deaths.

HMP Birmingham prisoners Demehl Thomas and Moysha Shepherd, both 25, are accused of boasting about drug dealing and violent assaults on rival gang members in the video, police said.
The pair are charged with making a sound recording in jail under the 1952 Prison Act.
They will appear via video link before magistrates in the city on Thursday.
West Midlands Police, which described the video as a "selfie rap", said it believed the prosecution against Thomas, formerly of Vernolds Croft in Highgate, and Shepherd, of Hampstead Road, Handsworth,  was the first of its kind.
Insp Nick Dale, said the law was intended to "minimise the potential" for a camera or recording device to be used inside prison "and possibly compromise security or pose a threat to the safety of prisoners and staff."

Geraldine Newman, 51, daughter Shannon, 11 and son Shane, six, were found on Tuesday in Allerton Bywater.
The children's father, Paul Newman, 42, from Normanton, was found dead on cliffs on Anglesey the same day.
Mr Newman was charged with common assault on Mrs Newman in July 2013. He received a custodial sentence, West Yorkshire Police said.
The assault case was assessed as high risk, subject to detailed review and monitored for 12 months.
During that time there were no further incidents reported to it, the force said.
There is also to be a full review of the current case, West Yorkshire Police said.
Mrs Newman was found in the house near Leeds and had died of head injuries, a post-mortem examination  showed. Her two children were stabbed to death.
Police said the case was "shocking". They are not looking for anyone else over the deaths.
Mrs Newman, a branch manager for Wilko in Castleford, was found downstairs while the two children were discovered upstairs.
Stacey Swinson, a daughter of Geraldine Newman, said: "What has happened to my family is absolutely tragic.
"I would like to thank everyone for their kind wishes and condolences.
"This is a very difficult time for us and I would ask that people respect our privacy while we continue to grieve with family and friends."
Mr Newman was discovered on a cliff ledge at South Stack, a rocky island about 180 miles away.
A father who killed himself and his sons in a deliberate house fire was identified by one of the boys as the culprit behind the blaze.
[NEXT_CONCEPT]
Two inmates have been charged with making a "selfie" rap video using a mobile phone smuggled into a jail.
[NEXT_CONCEPT]
A man suspected of killing his family in West Yorkshire had been previously jailed for domestic violence.