The Norwegian is said to have delivered a measured response.
The former Bhoys forward has been critical of the Scottish champions lately, also urging chief executive Peter Lawwell to either back or sack Deila.
But the Norwegian has responded by suggesting he is happy with how things are panning out at Parkhead.
Deila is quoted as saying in response to Sutton's accusations of Celtic producing 'bang average dross': "I think lately that we have had some performances that haven't been great. But that is the case with every team.
"You don't see any team that goes through a season without bad performances.
"But in Scotland we have won nearly every game that we have played. We have also scored a lot of goals. Again, it is not black all the time. Sometimes there are good things as well."
Is that a strong enough response from the manager of the Scottish champions?
Critics could be quick to point out an acceptance of low standards and a lack of ambition within Deila's tone. But that's for Celtic fans to decide. As long as the Norwegian is winning in the Scottish Premiership, what more can he do?
Those backing the Celtic boss can argue his lack of financial support in the transfer market make it far too difficult to compete in Europe, meaning he is simply doing the best he can with limited resources.
Which view is closer to the truth?