At one point some soldiers - all of them believed to be from the 1st Battalion The Light Infantry - appeared to kick a dead body.
Stills from the video footage caused shock around the Middle East when they appeared in the News of the World newspaper and were broadcast on several TV news channels.
'Mortar blasts'
The APA said in a statement the incident had been "thoroughly investigated" by the Royal Military Police.
"It appeared that four Iraqi civilians had been snatched from a rioting crowd and brought inside a military compound where they were assaulted.
"The video has a commentary appearing to encourage what was being done."
The APA said the footage also showed "immediately before the alleged assaults, the soldiers being attacked by mortar blast bombs and confronted by a riotous mob throwing stones".
The authority said it was only possible to identify two soldiers "apparently engaged in assaults footage".
But too much time had passed since the incident to allow a charge of battery, and there was insufficient evidence to allow more serious charges to be brought.
'Public interest'
Two servicemen could also have faced charges of committing "conduct to the prejudice of good order and military discipline" over "an alleged kick to the body of a deceased Iraqi civilian" and the commentary on the video.
"These charges do have a realistic prospect of conviction, but the APA took the view that the public interest did not require them to be tried by court martial," the authority said.
"They could be dealt with summarily by the commanding officer, or by internal army administrative action which can impose a range of sanctions including termination of service."
The APA has handed the case back to the Army to consider what action needs to be taken.