Celtic got away with dropping points last weekend when they drew against Motherwell because Rangers also managed a 1-1 draw against Aberdeen at Pittodrie.
Rangers also missed a big opportunity to secure a place in the knockout round of the Europa League when they only played out a draw at home against Aris Limassol on Thursday night.
However, Sutton is worried about Rangers and believes if they win the League Cup later this month then they could get a massive shot in their arm to try and cut down the deficit with Celtic.
He pointed out Celtic did the same from a similar position in Ange Postecoglou’s first season and believes like the Australian, Rangers boss Philippe Clement is saying the right things and is not shying away from making big calls on the pitch.
Sutton wrote in his column for the Daily Record: “Don’t get me wrong. Rangers’ poor showing against Aris Limassol shows they still have a way to go, but winning the League Cup would give Philippe Clement’s side a major shot of belief and added drive to try and overhaul a deficit in the table.
“Just as it did for Ange Postecoglou’s team in the Aussie’s first season when they came back from a similar position as now to win it.
“Clement is saying all the right things, just as Postecoglou did. And making big calls, as we saw with Todd Cantwell on Thursday night.
“Celtic need to stand on the pedal, get moving and strike fear into sides again.”
Rangers are eight points behind Celtic in the league table having played a game less than their Glasgow rivals.