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The club are still searching for their first point of the European campaign ahead of Thursday night’s Parkhead clash, which comes four days after a damaging 2-0 Premiership defeat at Falkirk.
Speaking on The Scottish Sun Sport’s Go Ballistic podcast, Boyd claimed O’Neill would rather have had a clear week to prepare for Sunday’s league meeting with Kilmarnock.
He said: “It’s not all rosy at Celtic. They look disjointed right now. I thought Martin was very spiky in his post-match interviews.
“They’ve got another European game on Thursday night. It’s another headache for Martin because he will just be wanting to get to next Sunday. Scott Bain had a fantastic afternoon, but I think, from Celtic’s point of view, you’ve got to look for more.
“The players have to shoulder some responsibility now, too. It looks like some results earlier in the season were probably papering over the cracks a little bit. I thought Celtic were outstanding against Motherwell and they were outstanding against Hearts.
“But then you feel as if there’s the performance in them that they produced against Dundee United and against Falkirk. I do feel as if the players are quite happy now to allow Martin to take the flak.
“Yes, the buck always stops with the manager. And Martin was telling the truth in his post-match interview when he said they’re still top of the table.
“But it’s maybe not what Celtic fans want to hear because they’ve just lost a game.”
Boyd believes the frustration among supporters goes beyond individual results, with Celtic’s recruitment and European ambitions also coming under scrutiny.
He added: “There is no doubt Celtic fans right now are looking at the bigger picture. The bigger picture is they have failed to recruit a certain level of player that will allow whoever the manager is to go and conquer in Europe.
That’s where the anger is coming from, and there will be memories of the Covid year when it all just came to a head.”