It’s been a disastrous seven days for the O’Neill’s side, losing 3-0 to Rangers in the League Cup, then 3-1 to Ferencváros in the Europa League on Thursday.
Celtic went to Ibrox hoping to get revenge on the auld enemy and extend their lead at the top of the Scottish Premiership.
Instead, the home side were worthy 1-0 winners thanks to a 33rd minute goal from summer signing Ryan Don Naderi.
Speaking to reporters after the game, O’Neill appeared to admit he was considering whether he will stay on as Celtic boss or not.
“I'm not immune from criticism. Far from it. Absolutely. They (fans) have every reason to ask, can you turn this round? Can you change the whole thing?" he said.
“It's not the first time I've been questioned about my managerial time. So, I'll have a look at it. I will reflect and see.
“Asking what I, myself, (can do), is the main thing. Asking what I can do to help the team. That would be the most important thing for me to see.
“I genuinely will reflect and see. It's a matter of whether I can help the team. If that's the case.
"The manager’s supposed to be able to do that. And, yeah, I will have a look at that there this week.
“That every single time that something crops up, things don't go so well, age plays a part. And you know what? They may well be right, you know?
“I'm 110 in two years' time, so, yeah, that might be a time to wrap it up. Listen, we've lost some big games. There's no question about it. I personally think every game here is big.
“We lost a European game. We lost the big match out in LASK. And, here, two defeats against us. Of course you have to question it.
“I will reflect on the games. I'll obviously speak to the board. And, you never know, they may want to speak to me. But I'll see.
“I've got some time to do that there. I will try and get a couple of days away and see how it goes.”