Celtic were embarrassed in Brendan Rodgers' first competitive match in charge.
Rodgers has so far utilised both 4-2-3-1 and 4-3-3 formations during his initial matches in charge of the Bhoys.
Leigh Griffiths, who scored 40 times last season, has generally been stationed as a right-winger in the system.
And Sutton feels that Celtic are missing a trick by not partnering Griffiths with new signing Moussa Dembele up-front.
“I’m not convinced about Griffiths out right. He’s a poacher and his best work is in between the posts,” Sutton said.
“I can’t understand what is so wrong about playing an old-fashioned 4-4-2 with wide men and a front partnership.
“Dembele and Griffiths could really complement each other.”
Griffiths has insisted that he does not mind playing wide-right, but he didn’t look at his most effective in Celtic’s first competitive match of the season earlier this week.
The Bhoys were beaten 1-0 by Lincoln Red Imps in Champions League qualification, with Griffiths failing to show his best in the fixture.
Rodgers seems unlikely to switch to a 4-4-2 formation any time soon, as he has rarely used it throughout his managerial career to date.
Celtic are next in action on Saturday in a friendly match against Wolfsburg, before they face the crucial second leg of their Champions League tie against the Imps on Wednesday.