Manager Neil Lennon had bemoaned the international fixture schedule that saw many of his players return to Glasgow less than 48 hours before their lunchtime clash at in-form Aberdeen.
And his squad suffered further disruption less than 12 hours before kick-off when a fire alarm went off at their hotel.
Celtic started slowly at Pittodrie although the home side could not make the most of some decent opportunities to put the ball in the box, but they got a grip of possession before the key moment just before the break when Aberdeen goalkeeper Jamie Langfield was sent off for conceding a penalty that Kris Commons tucked away.
Celtic, who scored late on through James Forrest, embarked on the seven-hour flight to Astana from Aberdeen Airport immediately after the match to give themselves as much preparation time as possible before Tuesday afternoon's first leg with Shakhter Karagandy.
But they should be able to cope with whatever comes their way in the former Soviet state after brushing off their late-night disruption in the Granite City.
Lennon said: "It's becoming a bit of regular occurrence in Aberdeen. The fire alarm went off about half one.
"It was freezing outside as well. I think it was somebody playing a prank but for some of the residents in the hotel it wasn't very nice.
"There were a couple of elderly people and people in wheelchairs who were a little bit distraught.
"It is tiresome but it can also fire you up."
Lennon's tactics showed the respect he held for Aberdeen following their opening Scottish Premiership wins over Kilmarnock and Motherwell as Efe Ambrose, Joe Ledley, Scott Brown and Beram Kayal all started in a narrow midfield.
Celtic struggled to break the Dons down initially but had created several half-chances before Charlie Mulgrew, who had moved up from central defence to swap with Ambrose, played a ball over the top for Georgios Samaras that led to the penalty.
Celtic goalkeeper Fraser Forster saved well from Niall McGinn just after the break and, although Celtic created a steady stream of chances, they were not fully comfortable until substitute James Forrest broke clear in the 87th minute to fire home via a major deflection off Mark Reynolds.
Lennon said: "The way we set up, we tried to stop (Peter) Pawlett, (Willo) Flood and (Ryan) Jack trying to influence the game. We lacked a bit of width but we were prepared to do that to influence the midfield more than them.
"Fraser didn't have much to do in the first half, he had one great save in the second half. We played into their hands a bit because we played a lot in front of them but we managed to turn them a bit as the game went on."
Lennon handed debuts to centre-backs Steven Mouyokolo and Virgil van Dijk, the latter from the bench. And although Adam Matthews came off with a tight hamstring, he hopes to have four more players to supplement his squad for the European clash with forwards Anthony Stokes and Amido Balde and midfielders Tom Rogic and Derk Boerrigter expected to return.
Meanwhile, Reynolds believes they showed the 20,017 crowd a more resolute Aberdeen side despite the disappointment of the result.
The defender said: "There has definitely been a buzz about Aberdeen and people have been talking us up.
"It's important as players that we keep that momentum going and keep putting in performances.
"That wasn't the result we wanted for the fans to come back but hopefully the ones who came that don't usually come saw a different Aberdeen side, an Aberdeen side that's going to fight and give 100 per cent and will not be outfought or out-muscled.
"If we get outplayed or don't get the breaks then so be it, but we should never be outfought or out-muscled."