The so-called friendly fire incident, 40 kilometres (24.8 miles) north of Basra, left one soldier missing, presumed dead, and another in intensive care on RFA Argus, the UK forces' hospital ship in the Gulf.
Another soldier who had been in one of the two destroyed Scimitar light reconnaissance tanks, manned by the Household Cavalry, escaped without injury.
Nursing shrapnel wounds and burns, the three injured soldiers, Lieutenant Alex MacEwen, 25, Lance Corporal of Horse Steven Gerrard, 33, and Trooper Chris Finney, 18, spoke of their bewilderment and anger.
They said the US pilot apparently failed to recognise that their tanks were a British make, with special coalition identification aids and even a large Union flag on another machine in the five-vehicle convoy.
Lance Corporal Gerrard said: "All this kit has been provided by the Americans. They've said if you put this kit on you won't get shot.
"We can identify a friendly vehicle from 1,500 metres [4,921 ft].
"You've got an A-10 with advanced technology and he can't use a thermal sight to identify whether a tank is a friend or foe. It's ridiculous.
I felt I was going to burn to death. I just shouted 'reverse, reverse, reverse'
Lance Corporal of Horse Steven Gerrard
"Combat is what I've been trained for. I can command my vehicle. I can keep it from being attacked.
"What I have not been trained to do is look over my shoulder to see whether an American is shooting at me."
The two Scimitars, followed by two armoured engineers' vehicles and another Scimitar light tank, set out on a "recce" of a road north west of Ad Dayr, north of Basra in southern Iraq, on Friday.
After coming under fire from Iraqi artillery, they were instructed to investigate a shanty town.
Troop leader Lieutenant MacEwen, 25, with special plastic bags now tied around his hands to treat his burns, described how the convoy tensed as villagers waving white flags approached from behind a large bank on the marshland by the Shatt al-Arab river.
"You could see the white flags above the bank but you didn't know whether they had any intention of surrendering or ambushing us," he said.
Lance Corporal Gerrard said he suddenly heard the distinctive, relentless roar of an A-10's anti-tank gunfire.
"I will never forget that noise as long as I live. It is a noise I never want to hear again," he said.
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"There was no gap between the bullets. I heard it and I froze. The next thing I knew the turret was erupting with white light everywhere, heat and smoke.
"I felt I was going to burn to death. I just shouted 'reverse, reverse, reverse'.
"My gunner was screaming 'get out, get out'. How I got out of that hole I don't know. Then I saw the A-10 coming again and I just ran."
Lying on his hospital bed, he said the A-10 circled and made a return attack run.
"On the back of one of the engineers' vehicles there was a Union Jack," he said.
"For him to fire his weapons I believe he had to look through his magnified optics. How he could not see that Union Jack I don't know."
The front two Scimitars, packed with hundreds of rounds of ammunition, grenades, rifle rounds and flammable diesel fuel tanks, exploded into flames.
One of the soldiers' colleagues, Lance Corporal of Horse Matty Hull, did not escape the explosion.
The British Scimitars have distinctive markings
Lance Corporal Gerrard also criticised the pilot for shooting when there were civilians so close to the tanks.
"There was a boy of about 12-years-old. He was no more than 20 metres [65.6 ft] away when the Yank opened up. There were all these civilians around.
"He [the pilot] had absolutely no regard for human life. I believe he was a cowboy. He'd just gone out on a jolly."
He added: "I'm curious about what's going to happen to the pilot.
"He's killed one of my friends and he's killed him on the second run."
Trooper Finney, who was hit in the leg when the A-10 made its second attack, said all the British soldiers and their families joked about "friendly fire".
He said: "I got a letter off my dad the day before the attack and it said 'Be careful, come home soon and watch out for those damn Yanks'.
"Looks like he tempted fate a bit there."
This is pooled copy from Patrick Barkham of the Times on RFA Argus in the Gulf.