Corporal William Savage, 30, from Penicuik, Fusilier Samuel Flint, 21, and Private Robert Hetherington, 25, both from Edinburgh, died in the blast.
They were killed on Route 611 in the Nahr-e-Saraj district on 30 April 2013.
The soldiers, who were in an armoured Mastiff vehicle, were unlawfully killed on active service, the coroner ruled.
Coroner, Darren Salter, will now write to Defence Secretary Michael Fallon.
The inquest was held at Oxfordshire Coroners Court.
Earlier, it heard that an improvised explosive device (IED) had been put in place using a tunnel and was triggered using a command wire from behind the 10ft wall of a nearby compound.
Post-mortem examinations concluded the three, who were with B Company, 2nd Battalion, Royal Regiment of Scotland, would have been deeply unconscious virtually instantly and unaware of what had happened.
Mr Salter said the Mastiff was designed to resist improvised explosive device (IED) attacks.
There had been earlier damage to this one, the second of three evolutions of the vehicle, in a strike in 2009.
However, there was "no significant evidence" that the vehicle failed to provide the "expected level of protection", Mr Salter ruled.
He also noted that experts referred to the size of the explosion as a "blast overmatch" and that the men were seated in the rear of the vehicle, which was nearest to the explosion.
The men died when an improvised explosive device (IED) tore through their heavily armoured Mastiff vehicle on April 30 last year.
The Royal Military Police made inquiries to the Afghan National Police about the incident, but no-one was arrested over it.
The Mastiff, a protective patrol vehicle, had gone from Forward Operating Base Ouellette to another base at Lashkar Gah Durai and was on its way back again when the attack happened.
There were four vehicles in the patrol.
The driver of the Mastiff, Fusilier Paul Howell, said in a statement that the regular locks to the rear doors had been faulty, and he had reported them twice.
He told the inquest that on the day in question, though they were stiff, they were fully sealed when closed.
Extra battle locks were not deployed, but they were not supposed to be when the vehicle was in open desert, only when there were potential public order situations, he said.
He said in his statement that there were 20 ammunition tins under the seats in the rear, which was normal.
The inquest heard that the IED was buried under the road, had been placed there by tunnelling, and was triggered by a command wire, probably from behind the 10ft wall of a nearby compound.
Sgt David Boxwell, who was in command of the patrol, said he had not been told of any problems relating to the place where the blast took place.
As for tunnelling under the road, he earlier said: "I had never heard of it before."
Company Sgt Major Steven Main said: "Everything we had had was off the tarmac road. IEDs were placed in the dust - it's easier to conceal."
He said there was no sign on the ground of the IED.
"The wire was so deep that we would not have seen it."
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