The former Celtic striker, in his current role as a newspaper columnist and analyst for BT Sport, has regularly handed out brickbats to Deila.
“The worrying thing for me is going forward,” he said. “The Champions League qualifiers are less than three months away. How is this team going to improve in ten weeks?
“Celtic need to get back to having an identity because, unlike Rangers, they don’t have one at the moment.
“Whoever the new manager is, I believe he’ll do better than Ronny with this set of players; he could hardly do worse. The quality of football is so bad now.”
Sutton believes that chief executive Peter Lawwell was wrong to appoint Deila and he is just as certain that he is making a mistake by allowing him to see out the season.
“We all know how important these Champions League qualifiers are,” he said. “I would’ve thought giving a new manager longer to prepare would have been better as it’s going to be difficult anyway.
“Had Celtic won [against Rangers] on Sunday and gone on to win the double it would just have been papering over the cracks. At least now people can see it. The failure to win big games had been going on for months, the fact they are one-dimensional.
“People say Deila is a good coach but he doesn’t have the ability to change things. We could all see what was happening, the players on the pitch all know what is going on, so why doesn’t the manager?
“If he had stayed, Rangers’ biggest asset next season would have been Ronny Deila. So Celtic needed to change.”
l Sutton was speaking at the Know Your Balls golf day at Mar Hall, an event to raise awareness of testicular cancer.