The Scottish champions were knocked out of the League Cup on Sunday after losing 2-0 to Ross County – their first cup defeat in 36 outings.
That result piled pressure on manager Lennon, whose side are also 11 points behind Rangers at the top of the Scottish Premiership and were dumped out of the Europa League in midweek.
In the aftermath of Sunday’s match, there were ugly scenes outside Parkhead, with fans gathering to call for the Northern Irishman’s sacking. Two police officers suffered minor injuries during a number of volatile exchanges, and Celtic have openly condemned the incident.
But focusing in on matters on the pitch, Bonner has argued that Lennon is not the sole cause of the Bhoys' disappointing output this term.
Speaking on BBC Sportsound, he said: “It’s going to be very, very difficult for him to stay in a job after that.
"I do feel sorry for him because he’s Celtic through and through, and he came in last term and almost got the club back after such a shock with Brendan Rodgers leaving. The players responded to him at that point in time, but they’re not responding to him now.
"You’ve got to question the attitude of the players. They switched off. I was shocked at half-time that they didn’t come out and have energy. They upped it a wee bit, but not enough.
"How many times did Ross Laidlaw have to make a save in that game? Nothing. Ajeti had one chance, one chance in the game – incredible. He’s playing up alongside Edouard, and how many chances did he have? He had a couple he scooped over the crossbar, [but otherwise] nothing, absolutely nothing.
"For me, you’ve got to point the finger at some of the players.
"Kristoffer Ajer, he was one that was talking about leaving the club and going to something big, but he’s still at the club, and he looks as if he’s not interested at times. He’s a young man who’s had such great times, and Celtic have put him in that position where teams were looking at him.
"They’ve gone so far back it’s incredible.”