The manager, Neil Lennon, talked of his side's task of reaching the group stages as not "insurmountable" while the midfielder Jo Ledley remained bullishly confident.
Despite a positive start to the match, Celtic found themselves behind in the 12th minute when slack defending allowed Andrei Finonchenko to score from close range. Next week's return in Glasgow became somewhat more difficult after Sergei Khizhnichenko headed in a second after the break.
"It is a big task but the tie is far from over," said a far-from-downbeat Lennon. "We have plenty in us to turn it around. The players will be very motivated. There will be a few players who will be disappointed with their performances tonight but we are still well in this tie although we have a lot to do. "I thought we did more than enough to take something out of the game in terms of goals. We had so many clear-cut chances but if you don't take them then the scoreline is always going to be a negative.
"I was disappointed with the first goal conceded because we talked about it at length, we went to sleep on the second touch. That, and the chances we squandered, just makes life really difficult for us, but it's far from insurmountable."
The "lack of composure" was the most disappointing aspect of the defeat for the manager. "We worked some great opportunities and all we needed was a goal to change the whole complexion of the tie. They didn't [surprise me]. We knew exactly how they would play. We knew they would be physical and a threat from set pieces.
"But if you look at the game in the cold light of day, we had six or seven clear-cut chances to either take the lead, equalise or get back in the tie so it gives us plenty of encouragement for the second game in Glasgow."
The home side walked round the pitch after the match, milking the applause of their fans, who were equally jubilant.
"I don't know [if they think it is over]," said Lennon. "But they have to come to Glasgow and they will have to defend well because we will come at them from the off."
The number of chances passed up was the principal reason given by Ledley for his belief that Celtic can turn the tie around: "We should have scored six goals easy," said the Wales midfielder. "To be fair to them, their keeper was on fire but we dominated possession and had more chances but lost sloppy goals. It is definitely frustrating, we dominated them away from home and two sloppy goals killed the game.
"Away from home you need to keep the door shut and it just wasn't good enough today. But we believe we can score against them."
Ledley played down the pressure Celtic will be under to rescue the tie. "There is always pressure in the Champions League, it is a massive tournament and fantastic to be in.Hopefully the fans will behind us and we will need to put on a good show."
Viktor Kumykov, the Shakhter coach, was applauded into the post-match press conference by local journalists but claimed his side's chances of representing Kazakhstan in the Champions League for the first time were only a little improved.
The Russian said: "We still believe Celtic have a chance to qualify and we believe the game in Glasgow will be even more difficult because Celtic are a more experienced team. We still have a chance - a little bit more of a chance than before the first game.
"We played very confidently but there is a second leg ahead of us and I hope we can get another good result. You need to play in a very disciplined and organised way and I think we did that.We believed after the second goal we had a chance to win the game but it is always hard to predict. You can never be sure about the final result."