The Bundesliga outfit began the Europa League game at Celtic Park as favourites to secure the win, but the return of Callum McGregor and Kyogo Furuhashi to the Celtic team raised hopes amongst the Bhoys faithful.
Leverkusen though ran out comprehensive 4-0 winners, scoring twice in each half to see off Celtic and claim all three Europa League group stage points.
Sutton thinks that the German were ruthless and exposed Celtic, who failed to take their opportunities.
He expects Postecoglou to stick with his system and style of play, and feels that the Australian must be given time to make his mark at Celtic Park, though he needs to eventually deliver.
“Celtic thumped by Bayer Leverkusen. Didn’t take their chances and exposed badly by ruthless Leverkusen”, Sutton wrote on Twitter.
“Ange has a style of play which he will stick with.
“I think he needs time and patience.
“Once the new players are bedded in though the team can’t keep making the same mistakes…”
Celtic are bottom of their Europa League group after picking up no points from their two games, six points behind top two Real Betis and Leverkusen.