Alvaro Negredo scored a hat-trick and Sergio Aguero struck twice as City qualified for the last 16 of the UEFA Champions League for the first time at the expense of the Russian side.
In-form CSKA striker Seydou Doumbia scored a goal in each half to make it 3-1 and then 4-2, but ruthless City were a constant threat and could have won by a bigger margin.
Slutsky reflected on a disappointing night at the Etihad Stadium that left his side six points behind City with two games remaining and unable to qualify due to their head-to-head record against Manuel Pellgrini's men.
The CSKA coach said: "Before the match we planned something to try and rebuff their attacks but we failed.
"It’s obvious, we made a lot of mistakes and there was a lot of freedom to attack but we were unbalanced in defence and when we had chances, we scored, but we should be alert because against such a good team you need to be – to lose concentration for a moment is fatal.
"Today we made a lot of mistakes. Obviously we were playing against players of a high level but those were our faults."
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