Stephen Hunt, 38, from Bury, was among 60 firefighters called to Paul's Hair World in Oldham Street in July 2013.
Jurors concluded it was probable two 15-year-old girls deliberately started the fire after smoking cigarettes at the rear of the building.
The case is to be reviewed to determine if any further action should be taken, police said.
The inquest heard how the teenagers made a "selfie" video in which they admitted starting the fire, which developed at a fire door and close to a cardboard storage cage.
The girls - who are now aged 17 and cannot be named - both told the jury they had put out their cigarettes.
A witness claimed one of the girls had admitted pushing a lit piece of paper through the doorway.
In the video, one of the 15-year-old girls, identified as Girl A, said: "We're not very happy because we started a fire we actually didn't mean to, seriously".
Girl B then added: "I put a flyer under. I didn't know it would set on fire. I saw a flame and ignored it."
Girl B was charged with arson but prosecutors dropped the charge three days before the trial, citing accidental ignition could not be ruled out.
Mr Hunt and a colleague, Jeremy Jones, had entered the building equipped with breathing apparatus but visibility was virtually nil, the jury was told.
Mr Hunt was found collapsed and could not be resuscitated. He was pronounced dead later that evening.
A lack of communication at handovers and briefings, a breakdown in radio communication, the internal layout of the building, inadequate fire risk assessment and acts of vandalism and criminal damage had contributed to his death, jurors found.
Senior coroner for Manchester Nigel Meadows said he would report the jury's findings to the Crown Prosecution Service.
Det Supt Peter Marsh, from Greater Manchester Police, said: "Following the findings from the inquest, GMP will now review the case with the Crown Prosecution Service to determine if any further action is to be taken."
A firefighter who died tackling a blaze in Manchester was unlawfully killed, a jury has concluded.