CSKA went into Wednesday's UEFA Champions League encounter at the Allianz Arena needing a victory as well as either a draw between Roma and Manchester City or a win for the latter to progress from Group E.
City triumphed 2-0 at the Stadio Olimpico, but CSKA's loss in Germany means they finish bottom of the pool and cannot even console themselves with a place in the Europa League in the new year.
Seydou Doumbia missed two presentable chances for the visitors during the first half, one a header before Thomas Muller's 18th-minute opener from the penalty spot.
The second opportunity was even more gilt-edged, the Ivorian hitting a weak finish into the legs of Manuel Neuer after finding himself one-on-one with the goalkeeper.
Late goals from Sebastian Rode and Mario Gotze rounded off what ended in a routine win for the home side, leaving Slutsky to wonder what might have been.
"In the first half we had some good chances to score," he said.
"You don't get many chances against a team like Bayern and we didn't take the ones that did come our way.
"We wanted to win but what could we do? I can't say any bad words about my players. They did all they could."
