The former Celtic striker has been impressed by one key aspect of the Bhoys' play.
And Sutton has credited Celtic's defensive solidity as their biggest improvement since this time last year.
Indeed, the 42-year-old believes the clean sheet Ronny Deila's men secured in the first leg against their Azerbaijani opponents is proof of how far they have come.
Sutton told the Record: "People, myself included, were critical of the amount of goals Celtic lost in Europe last season and were looking for improvement.
"If you take Wednesday as the benchmark they have improved and the clean sheet at home was crucial. They went on to nick the game and now have the advantage.
"I’d much rather be in Celtic's position than Qarabag’s. If Celtic nick a goal, the tie is surely done."
As Sutton states, the Bhoys' position is a strong one if they can score in Azerbaijan. There is no need for complacency, though, as a one-goal lead is always a slender one.
But the improvement the former striker has identified in Celtic's back line is no doubt an encouraging sign. Should Virgil van Dijk remain at Parkhead this season, the Dutchman can form a strong partnership with Dedryck Boyata, while the Hoops also have plenty of options at full-back.
Defending starts from the front, too, and Celtic's midfielders offer their back four plenty of support - something that will have to continue in Qarabag, where Deila's men should have plenty of opportunities to counterattack.