First-half goals from Sergio Aguero and James Milner looked set to condemn CSKA to a third consecutive defeat in Group E.
However, Seydou Doumbia pulled a goal back after the interval and a Bibras Natcho penalty ensured CSKA claimed a point and dented City's hopes of progression.
Slutsky felt the second-half display from his side warranted a share of the spoils, and expressed his pleasure at seeing CSKA get off the mark in a tough pool that also includes Bayern Munich and Roma.
"I can't say that we totally failed in the first half," he said.
"I don't remember City creating any good chances before their first goal.
"I am happy that we managed to show our mentality, quality and save a draw.
"It was clear from the very beginning that we are not favourites at all in our group. It's positive that we have already earned a point."
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