Marley Watkins scored the only goal in Ayrshire as Killie ran out worthy winners in the last-16 tie at Rugby Park.
A home draw in the quarter-finals of the competition awaits Derek McInnes' side, while Celtic's defence of their treble is already over.
"The goal, we switch off from the throw-in, we don’t win our duels and they go through and score. It was a disappointing result for us. But give credit to Kilmarnock. They worked very hard, put the tackles in, put the blocks in, and like I say, they win the game.
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