The 42-year-old believes that the Scottish Premiership leaders' situation is down to the club's board.
Former Celtic striker Chris Sutton has suggested that Ronny Deila is out of his depth at Parkhead, but insisted that the blame should be placed on the Hoops' board, rather than the Norwegian, the Daily Record reports.
Deila has come under pressure following a tough week for the club - which saw them knocked out of the Scottish League Cup, while Aberdeen cut their lead in the Premiership to just three points following their victory in the top-of-the-table clash - but Sutton believes that the finger of blame should be pointed much higher up.
Although the 42-year-old seems to suggest that the criticism the manager is receiving should be directed at the board, he has made it clear that, in his opinion, it is time for Deila to leave the club.
"Call it misjudgment or mismanagement, but letting things slide to this point has been a massive mistake. Ronny Deila is the one being panned right now, but it is his bosses and the rest of the Celtic board who must take the blame.
"I'm actually starting to feel sorry for Ronny. To my mind, he's a genuinely good guy and a nice fella, but the job of being Celtic manager is simply too big for him."
While the former Stromsgodset boss won two trophies during his first year at Celtic, the club's failure to make any kind of impression in Europe this season, as well as the fact that they only enjoy a slender lead in the league, highlights that they have not quite made the progress they would have liked in recent years.
Rangers' time outside of the top flight was arguably a real opportunity for the Hoops to ensure that they would be the dominant team in Scotland for several years to come, even after the Gers make their return to Premiership.
And while Celtic have won plenty of trophies over the last few years, this season suggests that they have not taken full advantage of the situation, leaving Deila's tenure to become blighted by comments from pundits and former players - like Sutton - who suggest that it was a mistake for the Norwegian to be appointed in the first place.