Alvaro Negredo scored a hat-trick and Sergio Aguero struck twice as City qualified for the last 16 of the Champions League for the first time at the expense of the Russian side, who got on the board thanks to Seydou Doumbia's double.
Slutskiy was frustrated with his side's mistakes which left them 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.
"Before the match we planned something to try and rebuff their attacks but we failed,” he said to reporters.
"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."
CSKA's only points in the group stages came from a win against Group D bottom side Viktoria Plzen, who they must now battle for third place and a berth in the Europa League.