That defeat followed a drab goalless draw against Kilmarnock last month and ex-Parkhead striker Walker believes the followers are now questioning whether the Norwegian can deliver.
“Celtic, at home, are normally very good. They had a difficult away game last week against St Johnstone and scored three goals, but in front of your own supporters I think you really need to send a message that you know what you are doing.
“And I think there is a growing feeling of resentment among the Celtic supporters that Ronny Deila might not be up to it.
“I have to say I still think Celtic will go on and win the title, they might secure another cup or two, but there is no evidence that Ronny Deila has the knowledge to get through the Champions League qualifiers next year.
The SPFL champions travel to Edinburgh to play Hearts on Sunday and Walker says they will have to be wary of Robbie Neilson’s side.
“They have managed to get that back. They still have great attacking players from middle to front. Jonny Hayes, Niall McGinn and Adam Rooney are all in fine form with Kenny McLean just behind them.
“However, I think Celtic’s strength, resources and ability to do business in the January transfer window will see them come good in the end.”