It is no secret things are far from rosy at Parkhead, with fan protests during almost every home match.
O'Neill is in charge until the end of the season - his second interim spell in this chaotic campaign - and cracks are starting to appear despite the Northern Irishman's legendary status at the club.
Supporters continue to demand boardroom change, there are obvious holes in O'Neill's squad and they have now lost seven league matches. That's as many as they lost in the previous two seasons combined.
Celtic fell behind to Felix Passlack's header and rallied to equalise through Benjamin Nygren's 18th goal of the season, but went down to 10 men after centre-back Auston Trusty was sent off for violent conduct.
Kai Andrews fired in a late winner for Hibs, making it successive defeats for Celtic after Thursday's Europa League reverse against Stuttgart.
"It's a setback, that's all it is," O'Neill said. "We're still in the race.
"I thought we were absolutely terrific. The players put heart and soul into the game. No complaints on that side whatsoever.
"We've been chasing for months now. There's not much room for error but we can still fight back. The players are disappointed but it's not over."
Despite O'Neill's defence of his players, others were less complimentary.
"It all changed with Trusty's sending off," Bonner said. "Hibs handled the game very well after that.
"Celtic couldn't get any momentum and it's a brilliant goal from Kai Andrews. Celtic didn't create anything. They ran out of luck."
O'Neill brought in Tomas Cvancara, Junior Adamu and Joel Mvuka to bolster his attacking options in January, but Adamu was an unused substitute against Hibs and Mvuka wasn't in the matchday squad.
"Without doubt, there is a lack of cutting edge at Celtic," Stewart said.
"What's up with Adamu? They need a goal and they put on [Daizen] Maeda, who is nowhere near the levels he was at before."

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