Celtic played out a 2-2 draw with the Turkish giants at home in the Europa League on Thursday evening.
The defending Scottish Premiership champions were actually 2-0 up at Celtic Park at one stage, but defensive mistakes forced them to settle for a share of the spoils.
The man responsible for Fenerbahce’s first goal was Efe Ambrose, who gifted an easy chance to Fernandao to pounce on.
The 26-year-old Nigeria international defender has made such mistakes this season, and former Celtic striker Sutton has asked why he started the game against Fenerbahce.
The former Chelsea and Aston Villa man has also questioned why Deila did not include 21-year-old defender Tyler Blackett in his starting lineup ahead of Ambrose.
Blackett, who joined Celtic on a season-long loan deal from Manchester United in the summer transfer window, came on as a substitute in the 82nd minute.
“But you have to wonder why Tyler Blackett didn’t start,” Sutton wrote in The Daily Record. “He was signed as a back-up central defender or full-back yet couldn’t get a game ahead of Ambrose.
“That suggests to me Deila doesn’t fancy him, which then makes you wonder who chose to sign him.
“Just who has the final say over signings is something that needs to be more transparent at Celtic Park because it’s clear the squad has been left severely short in key areas.”
Celtic will return to action on Sunday afternoon, when they take on Hamilton Academical away from home in the Scottish Premiership.
The Hoops are second in the league table at the moment with 20 points from nine matches, four points behind leaders Aberdeen with a game in hand.