The runaway Bundesliga league leaders were defeated 2-0 at the Emirates Stadium on Tuesday night to give Arsene Wenger's men their first European win and keep alive hopes of qualification for the knockout stages.
It was a third straight victory for Arsenal, who impressed in beating both Manchester United and Watford, with the north London club now second in the Barclays Premier League table, just two points behind Manchester City.
Walcott feels inflicting a first defeat of the campaign on Pep Guardiola's side will serve as a warning of Arsenal's intentions.
"You play against the best in the Champions League, Bayern are a top, top class team, but we showed our class," said the England international
"The confidence is just flowing through the team at the moment, you can see that
Results show that and if we continue this you never now where it is going to take us, but we are looking really strong
"We have been fantastic in the (Premier) League, the two games before in the Champions League weren't great, but the confidence is flowing through the team and you can just sense that, and I think a lot of teams are starting to be a bit wary of that
"That is what we want, we want to put out a message and (the result on) Tuesday night can hopefully show that
"But this result can't just be a one-off
We need to keep on doing it.
"However we have still got a lot to do (to qualify) and won't get ahead of ourselves because our focus now is on the Premier League."
Walcott added: " That (next Champions League tie in Munich) is a long way ahead, there are a lot of games coming up before that game, but again we believe we can beat anyone
If we beat Bayern, we can beat anyone."
Munich goalkeeper Manuel Neuer pulled off a remarkable first-half save from Walcott's point-blank header, but was eventually beaten when he failed to collect a deep free-kick as substitute Olivier Giroud headed into an empty net before Mesut Ozil added a second in stoppage time after the German had clawed the ball back from behind the goalline
Veteran Arsenal stopper Petr Cech also make some crucial saves, one early on from Thiago and then deflecting Robert Lewandowski's shot over just before Giroud broke the deadlock
Walcott is in no doubt of what the 33-year-old, signed from Chelsea in the summer, brings to the group, having made his first Champions League appearance for the Gunners.
"There have been a lot of top-quality goalkeepers, but the calibre he has brought to this club, and what he does off the pitch as well , which you guys don't see, just everything is just perfect," said Walcott
"It is just his whole manner and how he approaches the game and how he helps others
He is a team man, he wants people to do well and he has a lot of belief in this team.
"He makes massive saves in crucial times of the games and that is what lifts spirits and he shows why he has been at the top of his level for many, many years."
Source : PA
Source: PA