They have given themselves a mountain to climb, but it can be done.
Over in Kazakhstan they were playing in front of a relatively hostile crowd after a long journey - but the shoe will be on the other foot on Wednesday night and at least they know exactly what they have to do.
By all accounts, Shakhter Karagandy don't travel too well and, with a noisy crowd willing Celtic on, it is still possible to get the right result and progress.
So, for all those who have been vocal with their criticism, I feel it only fair to reserve judgment until the tie has been completed.
However, one of the big things for Celtic is that they can ill-afford to go into the game thinking about the consequencies of losing another goal.
You simply cannot afford to have thoughts like that in your head because it is a distraction and a mental drain. What they will have to do is approach the game intent on kicking off at a high intensity - and maintaining that throughout 90 minutes.
When I was manager at the club in 1983, I remember one Uefa Cup game where we went gung-ho and battered Sporting Lisbon 5-0 after losing 2-0 out there.
I do think the game has changed a lot since then and I'm not sure that you can really afford to set out your stall like that nowadays, but I do maintain that if you play at a high intensity it makes it very difficult for the other team to get any momentum - and to threaten.
I also don't necessarily subscribe to the view that Celtic need to get an early goal.
If you are playing in the right manner, pressuring your opponents and creating chances, the crowd will stay with you because they understand what you are trying to do.
Of course, it is vital that Celtic keep it tight at the back. It goes without saying that they cannot afford to concede another goal, but nor can they afford to think of what might happen.
They need to apply themselves and give the game full concentration - and they do have enough about them to go through.
I watched Tuesday night's game and I have to say that I thought Celtic's performance was not all bad.
It struck me as quite ironic that they put in a decent performance ye t still lost the game, whereas over in Sweden when they played Elfsborg the performance was poor but they still managed to get through.
I know there has been much said about the two centre-halves but I actually thought that goalkeeper Fraser Forster looked a bit nervous.
I felt as though he didn't use his influence the way we have come to expect from him and there were a number of occasions when he looked stranded in the six-yard box. Whether or not that is down to the fact he was playing in front of an unfamiliar backline, I don't know.
But what I would say is that Celtic dominated possession, created good chances and controlled much of the flow of the game.
That they lost 2-0 wasn't an entirely fair reflection of the 90 minutes and that is where the optimism will lie in terms of the second leg.
One of the big problems for Celtic was the long throw-ins and the high balls that Shakhter were launching throughout the game.
They will play like that again on Wednesday night and they will also sit back and defend with their lives, so it may be that Celtic will have to be patient.
Once you get that first goal there is every chance that you could feel some of that resolve disappearing.