"There was an ugly crime in which a large group of National Guards were martyred," he told Iraq's interim national assembly on Tuesday.
"We believe this issue was the outcome of major neglect by some parts of the multinational (forces)."
He gave no further details.
Al-Qaida linked Abu Musab al-Zarqawi had purportedly claimed responsibility on Sunday for the killing of the unarmed Iraqi soldiers who were dressed in civilian clothes and on their way home on leave.
The recruits were killed with shots to the head by fighters posing as police at a checkpoint.
A spokesman for the US-led forces in Iraq said only "terrorists" were to blame.
"This was a cold-blooded and systematic massacre by terrorists. They and no one else, must be held fully accountable for these heinous acts," he said.
The recruits were killed at a
bogus police checkpoint
"The Iraqi interim government is investigating this tragic incident. We will provide full support and cooperation to establish the facts and avoid repetition of similar events."
Allawi said he had ordered an investigation into the cause of the attack, one of the bloodiest yet against the country's fledgling security forces.
A source from his office said on Monday the government was probing whether the attackers had inside information on the movements of the victims and why they had no weapons or armed escort.
A senior Iraqi security source said it appeared the soldiers, based at Kirkush, 90km north-east of Baghdad, were ambushed by a large well-organised source with good intelligence.
The killings were a major blow to the interim government, which is trying to show its security forces will be able to ensure elections scheduled for January.