For the second season running, CSKA will face Bayern Munich and Manchester City in the group stages of Europe's premier club competition.
And the other side in Group E - Rudi Garcia's Roma - dished out a thrashing to the Russian side at Stadio Olimpico on Wednesday.
Gervinho scored twice in the first 31 minutes while Juan Iturbe and Maicon also added early goals to end the contest by the break.
CSKA rallied late - Ahmed Musa netted an 82nd-minute consolation before Georgi Schennikov hit the bar - but Slutsky was far from impressed.
"We started really badly but the problem was only in our mind - not physical," Slutsky said afterwards.
"Otherwise we wouldn't have ended the match like we did, growing in the last minutes.
"Roma are a really strong team and this match showed that we are not ready for a level like this.
"Having said that, if we'd pulled a goal back when they were 2-0 up, maybe we could have found further resources."
Life will not get any easier for CSKA, who host Bundesliga champions Bayern in their next Group E clash.
But midfielder Zoran Tosic has urged his team-mates to move on quickly.
"We knew we were going to play against a quality team and unfortunately we had a nightmare start," he said.
"After that it was impossible to come back into the game. We made so many mistakes and conceded four goals. We have to forget about this result."
