The Serie A side were fancied to cause an upset in Tuesday's Group E clash at the Stadio Olimpico after taking four points from tough matches with CSKA Moscow and Manchester City in their opening two matches.
However, Bayern produced an exhilarating performance and were 5-0 up after 36 minutes as two goals from Arjen Robben, strikes from Mario Gotze and Robert Lewandowski and a penalty from Thomas Muller ended the match as a contest by half-time.
Roma improved after the break and Gervinho deservedly got his name on the scoresheet, only for Bayern to step up a gear with a perfectly executed chip from Franck Ribery and a goal for fellow substitute Xherdan Shaqiri rounding off a fine performance from the Bundesliga champions.
Garcia refused to criticise his players, though, insisting it was his own tactics that proved Roma's downfall.
"It was a tactical collapse more than a psychological one. We weren't aggressive enough and allowed Bayern to play," Garcia told Sky Sport Italia.
"I am the first one who made the mistake, it is not the fault of the players, the first-half approach was my fault entirely. It was the wrong strategy, we should've been more closed up and try to hit them on the counter-attack.
"Once we were a goal down after 10 minutes, we ran forward and that played into Bayern's hands. We were too eager to get it back on track and left spaces that Bayern took advantage of. We should've kept our heads and waited for the right chance.
"We had a good reaction after the break, their goalkeeper prevented us scoring a couple more, but I am disappointed by the two goals we conceded late on. We wanted to prove there is pride in this squad and we did that in the second half."
Roma remain second in the group after City could only draw 2-2 at CSKA and Garcia is keen for his team to show they are better than Tuesday's performance showed.
"Now we must lift our heads and the only good news is Manchester City's draw, which allows us to stay second in the group," he added.
"Bayern were stronger than us and we played much less well than usual. We were almost spectators in the first half and what I don't like is the lack of aggression and unity.
"We must accept this defeat, which proves we also need more steps to get closer to the best teams in the world. We are still second and can hope for qualification, but certainly not playing like this.
"Playing against Bayern Munich there is only one thing to lose and that is with a slap to the face. Losing to them is normal."
