William Beal, nine, Antony Fothergill, five, and three-year-old Maddie Hudson died after being overcome by smoke and fumes in the blaze at their home in Bridlington.
Their 27-year-old mother Samantha Hudson spent months in hospital after being starved of oxygen and continues to be treated at a rehabilitation centre at Goole.
An inquest into the children’s deaths was told their mother had been to her sister’s birthday party and began drinking at lunchtime on November 11 last year. She visited several more pubs during the day and returned to her home, at 11pm, with friend David Hall, where her brother Mark had been looking after the children.
The three smoked cigarettes while having another drink but used improvised ashtrays including a salsa dip jar with water in it, because she had previously wanted to quit and threw out the ashtray.
The two men left and it is thought she then fell asleep on the floor of the living room, leaning up against an armchair.
Investigators concluded a discarded cigarette smouldered for a period of time, before igniting clothing, possibly school uniforms, which had been left under a bay window. The curtains then caught fire and quickly engulfed furniture, including armchair.
Fire investigator Steve Henry said: “I concluded that a carelessly discarded cigarette was the most likely cause of the fire. Samantha was sat in the living room, possibly asleep. She was woken by the fire or smoke alarm and went upstairs to aid her children. She gathered her children on the second floor bedroom. It was in this room the firefighters found the family huddled together.”
Mr Henry ruled out an electrical fault or candles and Humberside Police ruled out any suspicious or criminal act which may have caused the blaze.
Recording a verdict of accidental death on all three, Coroner Mr Saul added: “The loss of these three very young children can only be described as tragic. It is a word often used but it is a word which can only be used in these circumstances.”
The family declined to comment.