Corporal Mark Wright, 27, was killed when a mine exploded as a Chinook helicopter attempted to rescue a stranded platoon of Paras.
Coroner Andrew Walker, who recorded a narrative verdict following a two-week inquest in Oxford, said a catalogue of serious failures had contributed to his death.
He highlighted three factors - the lack of appropriate UK helicopters in Afghanistan fitted with a winch, the downwash from the Chinook sent to the minefield, and the administrative delay in sending a suitable helicopter.
Mr Walker said the lack of suitable helicopters was "lamentable" and "simply about money".
He added: "That a brave soldier is lost in battle is always a matter of deep sadness, but when that life is lost where it need not have been because of a lack of equipment and assets, those responsible should hang their heads in shame.
"This tragedy has its roots in the expectation that a small force of dedicated professional soldiers would be expected to extend the scope and number of their operations without the necessary support."
The inquest heard the Chinook was sent in to rescue troops from the Parachute Regiment's 3rd Battalion who were injured by explosions after a sniper strayed into the unmarked danger zone.
The marooned soldiers requested a helicopter with a winch be sent to extract the sniper, whose leg had been blown off, but were told none was available.
Instead the Chinook, which was not fitted with a winch, was dispatched but was waved away for fear of causing further explosions as it tried to land.
As it took off, a mine exploded, causing Cpl Wright, who was trying to help injured comrades, severe shrapnel wounds from which he later died.
Cpl Wright, from Edinburgh, was posthumously awarded a George Cross medal - the highest military honour for actions which are not in the face of the enemy. He was described by Mr Walker as an "exceptional soldier" who acted with "unhesitating courage in the most desperate circumstances".
Six others were hurt, including three who lost limbs, during the incident in the region of Kajaki in Helmand Province on September 6 2006.
Two American Blackhawk helicopters, fitted with winches, were eventually sent to rescue the soldiers - three-and-a-half hours after the first explosion was reported.
Following the inquest Cpl Wright's father Bob, accompanied by his wife Jem, said the family were given some peace of mind by the fact their son did not cause his own death or contribute to it in any way.
He said: "It has been painful to listen to the catalogue of errors that led to Mark's death.
"However, the coroner has made recommendations that must be followed. Jem and I don't want any other families to experience the loss of their child in similar circumstances."
The MoD has agreed to pay compensation to the Wright family and five of the soldiers involved in the incident.
Mr Walker listed a number of serious failures that contributed to the death of Cpl Wright.
He said the lack of batteries for radios at observation posts leaving soldiers having to resort to firing shots in the air to attract their colleagues "simply beggars belief".
He also criticised the teaching methods used to train soldiers to locate and mark mines which failed to take account of the technology available.
Other failures included no assessment of the mine threat, an officer's inability to interpret mine maps and the fact that the injured troops did not receive advanced medical treatment within the Nato doctrine of one hour.
Mr Walker made recommendations including that a mine training manual dating back to the Second World War be rewritten to include the latest technology.
Following the verdict, Commander of Joint Helicopter Command, Rear Admiral Tony Johnstone-Burt said he was confident that current resources enable British forces to meet the tasks that they face.
He added: "All UK helicopters deployed in Immediate Response Team roles on operations in Afghanistan are now fitted with winches as it is recognised that in certain situations they will be of use.
"However, we do not expect our forces to use helicopter winches to extract personnel from minefields because of the lethal risks involved."
Armed Forces Minister Bob Ainsworth added: "We have listened to the Coroner's comments and all of the evidence that was presented. I would like to reassure Cpl Wright's family that we are determined to learn all of the lessons that we can."
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