Celtic succumbed to a late Stuart Findlay winner as they lost at Kilmarnock on Sunday
Kris Boyd believes there is "a divide in the Celtic dressing-room" after sitting on the Kilmarnock bench during Sunday's 2-1 win over the champions.
Celtic manager Brendan Rodgers has admitted that the club's fans should be "alarmed" by his team's early-season league form.
And Boyd told BBC Scotland: "You only have to look at their performances.
"Are they really that bothered to be playing in a Celtic jersey right now? Not for me."
Suggesting behind-the-scenes problems, Boyd said: "I know there was a meeting after the Champions League exit.
"And, when you look at that, there is a divide in the dressing-room, there is no doubt about it. It was quite clear."
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The Scottish champions, enduring their worst start to a league season in 20 years, sold Moussa Dembele to Lyon on transfer deadline day despite Rodgers saying the striker would not leave without a replacement being signed.
But Dembele's fellow Frenchman, Olivier Ntcham, and centre-half Dedryck Boyata remained at the club despite reported interest from Porto for the former and a bid from Fulham for the latter.
Rodgers and Boyata subsequently had a public difference of opinion about whether the Belgium defender was fit to play in the Champions League qualifying loss to AEK Athens.
Boyd believes Ntcham's form has dipped in recent weeks and said: "When a club wants to play £14m for him, that guy's wages are going through the roof when he goes there. He wants to go. Boyata, the exact same.
"Ntcham was excellent up to the first four games. Since the transfer window shut and Moussa Dembele has gone, he looks a shadow of what he was."
'They're down a goal a game'
Kilmarnock have now gone four games without defeat against Celtic, with Boyd explaining: "We can afford to sit off the game, afford to have that low block, because they can't play through us and, once we get the ball off them, we can counter-attack.
"Celtic get frustrated on the ball and start doing things that they don't normally do."
Boyd thinks attacking midfielder Stuart Armstrong, who was sold to Southampton, has been "missed massively".
He also believes that, without Dembele, Celtic are lacking the type of target man they previously had in the shape of John Hartson, Chris Sutton and Jan Vennegoor of Hesselink.
"When you look at successful teams, they've always got a big striker," he said.
"When teams are struggling and stuffy in defence, you can throw that ball in the box and the big guy will go and challenge for it.
"In 38 league games in 2016-17, Celtic averaged 2.8 goals per game. The 22 games of this calendar year, they have averaged 1.5. That's down almost a goal a game."
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Highlights: Kilmarnock 2-1 Celtic
Source: bbc.com