Ronny Deila's record at Celtic is coming under scrutiny.
Deila has failed to get through the Champions League qualification stages during his two seasons at Celtic so far, and the Bhoys also were unable to win any of their six matches in the Europa League group stage this term.
With Celtic’s league form now also taking a turn for the worse, after a lose to Motherwell at the weekend, the pressure is heightening on the Norwegian boss.
And Walker said: "Celtic at home are normally very good. They had a difficult away game last week against St Johnstone and scored three goals but at home 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. European results have been embarrassing and there is no evidence he is learning from these European defeats.
"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 and for Celtic to lose out on that again would be a real hammer blow for the supporters."
Celtic’s lead at the top of the SPFL table has no been reduced to one point by Aberdeen.
The Dons have kept pace with Deila’s side, and they could go ahead of them over the Christmas period.
And Walker fears that the Bhoys will face a tough test next weekend, when they take on third placed Hearts.
"Sunday will be a tough one for Celtic,” the former Bhoys striker said. “It always is at Tynecastle and you have to be aware of what your nearest challengers are doing.
"Aberdeen have recovered well from that awful period in October where they had a five-point lead at the top and all of a sudden within five weeks it was a seven-point deficit.”
Celtic did win the double in Deila’s first season, but without the same level of domestic success this time around, it will be hard for the 40-year-old to keep his job.