Inflation has hit 4%, the highest for three years, with food prices rising, even of some items previously covered by the order, which banned below-cost selling.
Dan Boyle, Green Party finance spokesman, said: "Abolishing the order has had the effect those of us who opposed its removal said it would have - that of creating higher profit margins for the multiples."
He called for an independent investigation "to find out who has benefited from the abolition" but added: "That investigation must not be carried out by the Competition Authority, which acted as cheerleader for removal of the order."
His views were endorsed by Labour Party member Kathleen Lynch. She said abolition of the order had been "a total failure that has not helped lower prices one single bit".
Trade minister Micheál Martin, who repealed the ban, dismissed the criticisms as "simplistic" and said that the impact of reform would not take effect for at least a year.
Ann Fitzgerald, chair of the National Consumer Agency, said that the body would campaign against the "rip-off Republic".