Brendan Rodgers' Celtic side were beaten 1-0 by Anderlecht last night.
Boyata looked uncomfortable at the back throughout the game against the Belgian champions, as Celtic fell to a 1-0 defeat.
The Bhoys failed to play at a fast enough tempo to really trouble Anderlecht, who looked comfortable throughout.
And Sutton felt that Boyata dwelt on the ball too long on regular occasions.
“He is worrying the life out of me,” Sutton said. “Why is he taking a chance? Get it and give it to somebody who can play.”
Sutton’s comments were echoed by Brendan Rodgers, who suggested after the game that many of his Celtic squad had wanted too long in possession.
Boyata’s place in Celtic’s starting line-up could come under threat after the January transfer window, if Rodgers signs the centre-backs that he wants.
Celtic ultimately did enough to get through in the Europa League, despite not playing to their best.
Celtic just had to avoid being beaten by three goals to secure third spot in their Champions League group, and they did enough.
Celtic will now be playing European football in 2018, and that is an improvement on last season, when they finished bottom of their Champions League group.