The Socceroo midfielder returned from injury in the match, playing 26 minutes off the bench, as Celtic scored a late winner through James Forrest to down their Glasgow city rivals 2-1.
But ex-Hoops star Sutton was highly critical of Rogic's effort, claiming 'he looked about 85' and was a hindrance on his team when he came on to the pitch.
"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)."
It's not the first time Sutton has been highly critical of a situation involving the 26-year-old playmaker, with the Englishman expressing his displeasure at Socceroo's coach Graham Arnold last year after Rogic was called into Asian Cup camp and missed the previous Old Firm derby.
Rogic's substitute appearance against Rangers was his first for Celtic in 2019 after suffering a knee injury while playing for the Socceroos at the Asian Cup in January.
However, current Hoops boss Neil Lennon opted not to use Rogic in the 2-0 win against St Mirren on Tuesday night.
With former Celtic coach Brendan Rodgers leaving for Leicester City in February, Rogic has been linked with a move to the Premier League to join his ex-manager.