Following a tepid first match-up, the tie continued in similar fashion here as neither side was able to exert control or apply sustained pressure in the final third.
Ricardinho had the first shot of note as he took aim from 25 yards, but two deflections saw the ball trickle wide of Kasper Schmeichel’s post.
Celtic took time to grow into the game, but they were able to fashion the best chance of the half midway through the first half. A neat move down the left ended with Reo Hatate picking out James Forrest, whose header was tipped over the bar by Temirlan Anarbekov.
Kairat looked the better side as the opening period wore on, with the visitors struggling to get out of their own half at times.
Yet Rafael Urazbakhtin’s side couldn’t find a way through, going into the interval all square.
The hosts were handed their first major chance of the match shortly after the break when Schmeichel was caught out by a bouncing backpass and had no choice but to punch the ball clear from under the crossbar.
The resulting indirect free-kick was smashed goalwards by Jorginho, and despite the ball being blocked by Daizen Maeda's hands, Celtic survived the VAR check.
In a tie almost totally devoid of quality, a huge moment came for Celtic five minutes from the end of normal time. Callum McGregor slipped a delightful pass through to Maeda, who charged through on goal, but he lost his composure at the final moment and blazed his shot high over the bar as extra-time beckoned.
Celtic burst into life during the additional minutes as Luke McCowan, Benjamin Nygren, and Hatate all forced good saves from Anarbekov, but they couldn’t find the decisive goal, and the tie progressed to a penalty shootout.
The profligacy in front of goal continued into the shootout, with McCowan, Adam Idah, and Valery Gromyko combining to miss the first three spot kicks.
With Kairat leading 3-2 after four penalties apiece, Maeda was denied by Anarbekov to win the tie for the visitors, who were unsurprisingly delirious in their celebrations.
It is a historic moment for Kazakhstani football, while Celtic will be bitterly disappointed not to reach the tournament proper after only narrowly missing out on a place in the last 16 last term following their play-off defeat to Bayern Munich.
Flashscore Man of the Match: Yegor Sorokin (Kairat Almaty)
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- Kairat Almaty are only the second team from Kazakhstan to reach the Champions League
- Celtic have failed to win any of their last six away Champions League matches.