Ivory Coast striker Seydou Doumbia struck twice in the first half as CSKA stunned nine-man City 2-1 at Etihad Stadium on Wednesday.
Doumbia wreaked havoc against the Premier League champions, opening the scoring courtesy of a powerful header just two minutes into the contest.
Yaya Toure, who was sent off in the second half, restored parity six minutes later via a sublime free-kick, only for Doumbia to restore the Russian champions' lead in the 34 minute as a result of some questionable City defending.
"We played our number two and we were hoping to counter-attack. Our plan worked," Slutsky told reporters afterwards.
"We had chances in the first and second half and we're happy that our plan worked."
CSKA, who won in England for the first time, leapfrogged City into third position, level on points with second-placed Roma heading into the final two matchdays.
"I think we have become stronger [from last season]. Last year, we had many players who weren't as good as those this year," Slutsky added.
"And this year, we have many more strong players. We were relying on the players who are strong in the Russian League as well."
Slutsky, though, admitted recovery may have worked against City in the lead up to Wednesday's fixture.
City were 1-0 winners in the Manchester derby on Sunday, while CSKA had an extra day to recover having lost 1-0 to Russian rivals Zenit on Saturday.
"In the current situation, they had a very tough match against Manchester United over the weekend, and they probably didn't have enough time to recover and we had one extra day to recover," Slutsky said.
"So, that probably plays a part as well."
