She said the coroner had recognised the "importance of the issues" and she would be "watching" to make sure the MoD implemented his recommendations.
The coroner read out a narrative verdict, which is a statement about how death occurred, used when a coroner believes the conclusions require detailed explanation.
Relative Sarah Chapman: 'Systemic failings in the MOD caused the deaths'
He recorded verdicts of "unlawful killing by terrorist insurgents".
Mr Masters said: "The failure to fit ESF [explosion suppressant foam] was on the facts found a serious systemic failure and a contributory factor in the loss of the aircraft.
"There was a loss of opportunity for the survival of the crew by that failure."
Among Mr Masters' recommendations was for all RAF combat aircraft to be fitted with fuel tank inerting systems - which do the same job as ESF.
He said, in particular, the Hercules' successor, the Airbus A400M, must all be fitted.
Armed forces minister Bob Ainsworth rejected the coroner's verdict of "systemic failure" and said the MoD did a "tremendously challenging job".
He told BBC Radio 4's PM programme the fitting of explosion suppressant foam (ESF) had not been given top priority in the period before the crash.
That decision was not amended as the nature of the threat facing aircraft in Iraq changed, said Mr Ainsworth, adding: "To that extent, we failed these people. There is no doubt about that whatsoever."
He said the MoD had learned "a lot of lessons" as a result of what happened and all aircraft operating in dangerous environments were now fitted with ESF.
Mr Masters also said the crew had been "failed" by a system which meant intelligence of insurgent activity did not reach them.
John Hutton says lessons have been learned from the tragedy
Two US helicopters had been shot at in the same area by Iraqi insurgents just hours before.
The inquest heard that an e-mailed incident report was left unopened by an unnamed British intelligence officer.
He said he did not open it because he had no idea the aircraft, which was on a special forces mission, was even in that area at the time.
This should "never be allowed to happen again", the coroner said, recommending a review of coalition intelligence procedures.
Summing up at Trowbridge town hall, Mr Masters said the two-month hearing had been "plagued" by lax RAF record-keeping and criticised its policy of shredding documents.
He also levelled criticism at the US military for not authorising interviews with American eyewitnesses.
Aside from an Iraqi, US servicemen were the only eyewitnesses to the incident on 30 January 2005, but they were not available for interview.
"The stance taken by the US is difficult to comprehend," said the coroner.
"I just wonder, what if the boot had been on the other foot - if a US aircraft had come down with the loss of 10 lives and the only eye witnesses had been British forces?"
The Hercules C-130K, flight XV179, from RAF Lyneham's 47 Squadron, was shot down by enemy fire from a medium-calibre anti-aircraft weapon.
It hit a fuel tank in the right wing, causing the ullage - the highly flammable fuel-vapour-and-air mix created as fuel is used - to explode and blow off half the wing.
The plane was flying at low level, through a known ambush zone
It crashed into the desert, 25 miles (40km) north-west of Baghdad.
Witnesses told the inquest the crew were flying low (about 150ft; 46m) to avoid the threat of surface-to-air missiles.
Recalling evidence that had been heard, the coroner said three reports in the 1990s all said wing-located fuel tanks carried ullage explosion risks.
In 2002, a research report, sent to senior RAF figures, said that Hercules' wing tanks were the most vulnerable part of the planes, liable to explode if hit by small arms fire.
The report said "a potential solution to reduce risk is to retro-fit all C-130 aircraft with dynamic foam for the wing fuel tanks".
The coroner said: "Effectively, in my judgment, this means: 'Get on and do it'.
"Despite all the recommendations, a decision - unrecorded - was taken not to proceed.
"All the other recommendations in that report were approved, but this was not, and I consider that to be significant."
A second report, in 2003, said the recommendation still applied. Yet it was not acted upon until after the tragedy in 2005.
American Hercules have had ESF since the 1960s.
The 2005 crash was the largest loss of life to the RAF in a hostile act since World War II.
The crew, who were mainly based at RAF Lyneham in Wiltshire, were: RAF 47 Squadron's Flt Lt David Stead; 35; Flt Lt Andrew Smith, 25; master engineer Gary Nicholson, 42; Flt Sgt Mark Gibson, 34; Flt Lt Paul Pardoel, 35; chief technician Richard Brown, 40; Sgt Robert O'Connor, 38, Acting L/Cpl Steven Jones, 25.
The passengers were: Sqn Ldr Patrick Marshall, 39, from Strike Command Headquarters and Cpl David Williams, 37.
EXPLOSIVE SUPPRESSANT FOAM SYSTEM
1. Without foam: Explosive mix of fuel vapour and air above liquid fuel ignites easily. Once this ignites, a compression wave pressurises the remaining gas, increasing the explosion.
2. With foam: Foam expands to fill space in tank as fuel level drops. Vapour ignition is confined to the area close to spark, stopping explosion.
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