A ten-day inquest in Salisbury, Wiltshire, heard the two soldiers, who served with the Royal Logistic Corps, were sleeping in a tented Transport Troop office so they could respond more quickly when supplies arrived.
After finding that a smoke detector in the tent was not working, that the tent only had one exit and that senior commanders and fire safety officers did not know soldiers were sleeping in the tent, coroner David Ridley listed seven areas where there was either a "systemic failure" or "failure" in the circumstances that led to the men's deaths.
Speaking after the hearing, Pte Hutchinson's parents, Paul and Elaine, and brother, Liam, said: "Dean was a soldier and we will also be immensely proud of the fact he served his country but we feel that he should never have lost his life in the way he did out there in Afghanistan.
"We are pleased that the coroner's conclusion reflects the Army's incompetence in not carrying out the correct procedures to ensure Dean's safety."
Fighting back tears, Mrs Hutchinson added: "God bless both our boys."
Eyewitnesses described to the inquest smelling smoke coming from the area housing a 32in flat-screen TV, boiler and fridge, and seeing flames coming from cabling leading to an air conditioning unit.
But there were delays in alerting the military fire brigade because soldiers at the scene did not know the emergency 222 number.
Fire investigators concluded that the blaze started in the vicinity of the electrical appliances and quickly spread.
Had both senior commanders and fire safety officers known that soldiers were sleeping on duty during night shifts, the fire risk assessment for the tent would have had to have reflected it, with separate sleeping areas and an unobstructed rear exit.
The inquest heard there may have been confusion about who was responsible for checking smoke detectors in the tent.
Electrical items in the Transport Troop tent had not been PAT tested, although regulations stated it should have been done.
Other witnesses spoke of the dangers of "daisy chaining" multiple extension leads, which had been the cause of a previous fire at Camp Bastion.
Since the tragedy a number of changes have been made by the Ministry of Defence and Army to improve safety for troops using tents.
Mr Ridley listed seven "contributory factors" in the deaths of the two soldiers during his lengthy narrative conclusion.
*The systemic failure by the chain of command to communicate the occurrence of sleeping on duties at night to key personnel.
*The failure to police the occurrence of sleeping on duties at night through the use of random checks.
*The failure to effectively check the working functionality of the nine-volt smoke detector located inside the tent where the fire started, resulting in it not being in working order at the time of the fire.
*The systemic failure to provide effective training, especially to fire NCOs, to identify the potential risk of the overloading of sockets and extension blocks.
*The failure to rectify the error in the December 2010 fire risk assessment, when it became known that sleeping was taking place within the tent in December 2010.
*The failure to request a fresh fire risk assessment following structural alterations.
An Army spokesman said: "Our thoughts remain with the families of Private Dean Hutchinson and Private Rob Wood.
"The coroner has identified a number of failings that contributed to their tragic deaths for which we are very sorry.
"A number of improvements have been made to fire safety procedures since 2011 but we will study the coroner's recommendations to ensure everything is being done to reduce the risk to personnel and prevent future incidents."