Nasar Ahmed, who had severe asthma and multiple allergies, died after falling ill in the supervised detention room of Bow School, Tower Hamlets, in November
The 14-year-old ate a meal he was allergic to hours before he collapsed.
Nasar's mother accused staff of failing in their duty of care. Bow School said it had reviewed its safety procedures.
Coroner Mary Hassell said it was a "possibility but not a probability" that had adrenaline been administered and speedier use made of an EpiPen, Nasar might have been saved.
Ms Hassell said she would be writing five Prevention of Future Death (PFD) reports, including one to the Chief Medical Officer to ask if EpiPens should be provided alongside defibrillators in public places.
The coroner found that school staff had underestimated how serious Nasar's asthma was, listing it as mild to moderate, rather than severe.
They were also unfamiliar with pupils' care plans, unless they were due to take the children on an excursion.
Ms Hassell said that staff members' lack of familiarity with Nasar's medication box, and the omission of any mention of an EpiPen or adrenaline in his allergy action plan, had "used up time in an extremely critical situation".
Nasar's parents said they were "deeply saddened" to hear of missed opportunities to save their son's life.
The inquest heard staff had failed to properly administer the 14-year-old's medication in the five minutes before paramedics arrived.
What staff did to help Nasar
In the case of adrenaline, school staff were advised by phone to wait for emergency crews to administer it, but the coroner said one dose was unlikely to have caused him any harm, whereas "the potential good of giving an EpiPen is lifesaving".
Speaking outside Poplar Coroner's Court earlier, Nasar's mother Ferdousi Zaman said: "If he has anaphylaxis I give him his EpiPen.
"They [school staff] are first-aiders, they are more knowledgeable than me."
"They have failed their duty of care."
In a statement, his family said: "It has been extremely difficult to sit through the evidence of our son's last conscious minutes.
"To hear about his fear and panic, and his struggle to survive will haunt us forever."
The family has called for a review into the care of pupils with asthma and allergies.
The Year Nine pupil had asthma, severe eczema and a host of allergies to milk, fish, nuts, wheat, apples, oranges and some meats.
On 10 November he consumed a school dinner of tandoori chicken made with milk.
Staff at Bow School tried to save him as his condition quickly deteriorated and the teenager from East London died four days later in hospital.
Cath Smith, the executive head teacher at Bow School, said: "We are all deeply saddened about this tragic incident and continue to offer our heartfelt sympathies to Nasar's family.
"The safety of those in our care is of course, our overriding concern, and following Nasar's death we rigorously reviewed all of our safety procedures and are providing more training for staff across the board.
A pupil who died after falling ill in detention could possibly have been saved if he had received medication more quickly, a coroner has concluded.