Arjen Robben, Mario Gotze and Thomas Muller scored for the Bundesliga giants, who had briefly been pegged back to 2-1 when Keisuke Honda struck from the penalty spot.
Bayern and Manchester City are through from Group D in the UEFA Champions League, and Slutsky said his team were well below two of Europe's best sides.
"We were drawn in the same group as categorically the best team (Bayern) in Europe," the 42-year-old said.
"I think Manchester City are also one of the best, considering their current situation.
"I wouldn't say we failed in our away matches but we haven't been good enough to pick up points. We played pretty well and we fought well at home against some of the best sides in the world."
Slutsky was proud of his team's second-half performance at the Arena Khimki but said they failed to take their opportunities.
"Unfortunately, we didn't make the most of the chances we created," Slutsky said.
"Today it was all about converting chances because it's hard to create many if you play against Bayern.
"Both teams looked sharp and we didn't have any fewer chances than our opponents. I'm very proud of the way we played in the second half."
Midfielder Pontus Wernbloom rued the mistakes made by his side and said it was always going to be tough to win after conceding the first goal.
"It was a tough game, of course, but I think we should have scored more than one goal," the Swede said.
"We had a lot of chances and could have won but we gave away the goals and against a team like Bayern you cannot make the mistakes we made today.
"We made two or three errors and they killed the game. We didn't (score early) and that was the story of the night for us since they took all their chances."
