Former Celtic striker Andy Walker has been unimpressed by their "dull" play and questioned whether manager Ronny Deila can deliver the improvements needed in Europe.
After eventually finishing bottom of their Europa League group, the Scottish champions have stuttered in the Premiership.
Saturday's 2-1 home defeat by Motherwell made it four games in a row Celtic have failed to win at home, ratcheting up the pressure on manager Deila.
"Their style of play is pretty dull," Walker told Sky Sports News. "It's uninspiring.
"Motherwell were ambitious under Mark McGhee, very energetic, and played with a couple of strikers as well.
"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.
"The European results have been really embarrassing and there is no evidence that he is learning from these European defeats.
"I have to say I think Celtic will still 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 yet again would be a real hammer blow for the supporters."
Aberdeen's 4-0 win at Kilmarnock saw them cut the gap on leaders Celtic to one point and they could go top on Saturday at home to Inverness, 24 hours before the Hoops face Hearts.
Walker said: "That will be a tough one Tynecastle, it always is, and you have always got 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 of the Premiership and all of a sudden within five weeks it was a seven-point deficit.
"They have managed to get that back and they still have got 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.
"So if Aberdeen can put a run together like they did at the start of the season, hopefully they could push Celtic all the way.
"But I think with Celtic's strength, resources and ability to do business in the January transfer window, I still think Celtic will come good in the end."