They lost 3-2 to Yelimay Semey despite initially leading by two goals.
The defeat marks only their third loss in 20 top-flight matches this season.
Head coach Rafael Urazbakhtin made five changes to the team that travelled to Slovakia for a penalty shoot-out win against Slovan Bratislava midweek.
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Brazilian summer signing Edmilson scored both of Kairat’s goals.
The reigning Kazakh champions now face a 7,000-mile round trip to Scotland to play Celtic in the Champions League play-off.
Celtic come into the match following a 4-1 victory against Falkirk in the Premier Sports Cup on Friday night.
Daizen Maeda, Alistair Johnston, and Dane Murray were among the goals.
Celtic manager Brendan Rodgers remains hopeful of adding to his squad before the first leg against Kairat.
Rodgers said: “It would be great.
“We’ve obviously named a squad, but right up until just before the game we can do that.
“So that would be really good if we can.”
The deadline for two further additions to the 25-man squad submitted to UEFA expires at 11pm on Tuesday night.
Celtic will be looking to carry their cup form into the crucial Champions League play-off against Kairat.
The outcome of this two-legged tie will determine who progresses to the league phase.
Both teams will be eager to make a strong start in the first leg.