Rogic was brought on as a second-half substitute at Parkhead and failed to impress an expectant Sutton, who went so far as to suggest the 26-year-old's presence was akin to playing with a man down.
"It was 10 against nine because Celtic put Rogic on, who looked about 85," Sutton said on BT Sport's Scottish Football Extra.
"He was moving around like an OAP (old age pensioner)."
Sunday marked the Rogic's first Celtic appearance of 2019 after a serious knee injury sustained at the AFC Asian Cup left the midfielder needing surgery.
Despite Sutton's displeasure, Rogic played the final 26 minutes of the match, with James Forrest on hand to snatch a 2-1 victory in the closing stages.
Sutton is no stranger to controversy, having previously launched a scathing attack of the Socceroos' Asian Cup campaign saying: "It's Mickey Mouse football. Stick to your prawns and your BBQ's Australia."
