Major General Tim Cross said Iraq's military was blighted by poor leadership and a lack of cohesion.
The former commander, who was Britain's most senior officer in planning for the 2003 Iraq invasion, said: "Churchill said back at the beginning of the 20th century, you can destroy an army very quickly, and effectively we did that when we disbanded the Iraqi military back in 2003. It can take a generation to build a strong, capable military that is going to win this sort of campaign."
His comments followed those of Lord Dannatt, the former chief of the general staff, who on Monday urged the British Parliament to debate deploying up to 5000 soldiers.
Carter said that the fall of Ramadi, 95km west of Baghdad, showed that "we have an issue with the will of the Iraqis to fight Isil [Isis] and defend themselves".
Ramadi's defence melted away as Isis advanced earlier this month. Hundreds of policemen were killed after Iraqi troops withdrew. The US responded with limited airstrikes on the city's fringes. Months of airstrikes and the deployment of advisers to reform and train the security forces have failed to keep up with Isis' aggressive tactics.
Iraqi leaders expressed disbelief at the accusations. A military commander in Anbar described Carter's comments as "a provocation to the Iraqi Army and Iraqi people designed to make people lose their trust in the army".
Rare birds threatened
• The capture of Palmyra by Isis may cause the extinction of a rare breed of bird.
• A tiny colony of the northern bald ibis was found near the city in 2002. It was home to seven of the last wild population in the Middle East. When the colony's guards fled the jihadists last week, the birds were abandoned.
• The Society for the Protection of Nature in Lebanon is offering a reward for information on the female, which is understood to be the only bird that knows the migration routes to wintering grounds in Ethiopia.