Away goals from Toni Kroos, Thomas Muller and Mario Mandzukic mean Arsene Wenger's side will have to score at least three times at the Allianz Arena to have any hope of progressing to the quarter finals.
And while the England international admits it will be "very difficult" to beat the Bundesliga leaders on their home turf, he still thinks the Gunners can have a successful finish to the Premier League campaign if they regain their confidence.
"We have to be realistic and say it's going to be very difficult [to progress in the tie]," he told Goal.com. "[Bayern] are very strong at home, we need to score three goals, and we can do that if we work hard and show what we did in the second half anyway.
He added, "I hope the guys don't dwell too much on this result today; I think we need to get back to where we should be in the league. We have had some very positive results in the Premier League so we need to start believing again and start climbing up the table."
Arsenal started the game brightly but were 2-0 down in 20 minutes, and despite Lukas Podolski's header hinting at a comeback, a late third put the Germans firmly in control of the tie - with Walcott saying it could be a "killer blow."
"It was a disappointing result losing 3-1," he continued. "I felt we started off the game quite well to be honest, but I thought Bayern [Munich] took their chances, they were very strong, very well organized.
"We came out quite strong in the second half there are a lot of positives we can take from that. We thought when we got that goal unsteady them slightly which it did to be fair but we had a great opportunity to get back to 2-2 and then three minutes later they got the killer blow.
"I felt if it did stay at two we would have a great chance [in the second leg], but 3-1 is a difficult ask. We are going to be positive, we have to concentrate on [Aston] Villa now, we've got some important games in the Premier League coming up."
The Gunners are currently in fifth place in the league table, four points adrift of fierce rivals Tottenham in the race for a Champions League qualifying place.