Last season, Celtic failed to win a game in the Champions League group stage and finished bottom of their group with only two points.
The Scottish giants are set to play Lazio, Atletico Madrid and Feyenoord this season in the Champions League group stage and Rodgers will be determined to prepare his team to face the European elite.
Sutton is of the view that the Bhoys faithful will want to see Celtic not being outclassed in Europe this season and stressed that the fans will want to see some progress.
The former Celtic star admitted that Celtic’s opponents in the Champions League group stage are not easy ones and thinks that Rodgers will face an acid test in Europe.
“Listen, there’s much more to do”, Sutton wrote in his Daily Record column.
“The Champions League is going to be an acid test for the manager and fans will want to see progress.
“It’s going to be extremely tough to make a dent against Atletico Madrid, Lazio and Feyenoord, but Celtic have to try to make some inroads.
“Not be outclassed and do themselves justice while sticking some points on the board.”
The Parkhead outfit defeated Rangers at the weekend to take a four-point lead over their city rivals in the Scottish Premiership.