"We made a lot of mistakes," Sky Sports News quotes him as saying. "Obviously we were playing against players of a high level, but those mistakes were our fault.
"We lost because of ourselves, while in Bavaria (where CSKA lost 3-0 to Bayern Munich) it was mostly down to the level of the other side.
"How can you be psychologically ready when after the first minute you concede a goal and then three goals during the first half?"
Slutsky also highlighted his side's defensive problems against the former Premier League champions.
"There was a lot of freedom to attack but we were unbalanced in defence," he said. "Obviously when we had chances we scored but we should be quite alert.
"With such a tough team as Man City you have to be alert because they can be fatal in a split-second."
CSKA are currently third in Group D with three points from four matches.