Occupation Watch, an international group of peace and justice organisations set up to monitor the conduct of occupying forces in Iraq, said the process for Iraqis to make claims was purposely opaque and often their treatment by the US military bordered on cruelty.
"There is a culture of impunity," Occupation Watch's researcher Paola Gasparoli said on Saturday.
"Many of the most important cases cannot be presented or are being rejected for entirely illogical reasons," she said.
After major combat was declared over on 1 May, the US military said it would hear claims from Iraqis whose family members were killed or wounded in incidents involving US troops as long as they took place in non-combat circumstances.
According to Human Rights Watch, the US military received nearly 5400 claims as of mid-September, of which 4148 had been adjudicated and 1874 denied.
The US claims it has paid out several million dollars in compensation.
But Occupation Watch insists the claims process lacks clarity.
"Many of the most important cases cannot be presented or are being rejected for entirely illogical reasons"
"Sometimes soldiers know they have killed someone wrongly, so they do everything to make sure they get away with it," Gasparoli said.
"There have been cases in which bodies were stripped of identification and delivered to hospitals as unknowns," Gasparoli said.
"We need to work to put pressure on the US army to change the claims process and to start to take some of these claims seriously, instead of just dismissing them," the researcher argued.
Between 7900 and 9800 Iraqi civilians are said to have died in war-related causes since the invasion.
In a 30-page report covering three months of research, Occupation Watch has listed several serious cases of claims it has followed. None of these claims for compensation has been successful.