The Scottish champions started the match positively but found themselves behind in the 12th minute when Andrei Finonchenko took advantage of some slack defending to score from close range.
The visitors missed a series of chances before and after striker Sergei Khizhnichenko headed in a second after the break to leave the shell-shocked Hoops having to make amends against the Kazakhstan side in next week's second-leg in Glasgow.
The Parkhead boss, though, was far from downbeat afterwards.
"It is a big task but the tie is far from over," he said. "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 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 but that and the chances we squandered, it just makes life really difficult for us but far from insurmountable."
Asked about the most disappointing aspect of the defeat, the Northern Irishman replied: "Just the lack of composure at the final bit, really, because 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 the former Celtic skipper. "They are definitely in the ascendancy and there is that euphoria straight after the final whistle. But they have to come to Glasgow and they will have to defend well because we will come at them from the off."
- Sports & Recreation
- Andrei Finonchenko
- Sergei Khizhnichenko