Despite losing 3-0 to Real Madrid at home, Celtic took the game to the European champions and created a number of opportunities against them.
They were the more dominant side against Shakhtar Donetsk this week and many believe the Scottish champions should have got more than the 1-1 draw against the Ukrainian side.
Sutton stressed that Postecoglou is leaving a lasting effect on Scottish football with his team’s performances and he is changing the perception of Scottish teams in Europe.
He admitted that before Celtic’s brave performances in the Champions League this season, Scottish teams were always expected to be defensive in their away European commitments.
The Celtic legend believes Postecoglou’s side have shown that they can more than compete at the level going forward.
Sutton wrote in his column for the Daily Record: “Postecoglou is ripping up the perception of the Scottish game all over Europe.
“He’s doing to Scottish football what Pep Guardiola did for the English game.
“It’s a completely new approach that’s almost unheard of up here.
“We’re used to seeing our teams going abroad and trying to shut up shop and hoping to hang on for results.
“Celtic went out and imposed their game on their rivals. It’s bold, but you know what? It just might work.
“We’ve already seen enough to suggest Celtic can compete at this level.
“If you can create that many chances against Madrid and Shakhtar then you can carve out opportunities against anyone.”
Celtic will next be in Champions League action again in October when they travel to Germany to take on RB Leipzig.