The second-choice left-back, who performed admirably in his duel with Arjen Robben, was delighted to be picked for the crunch clash and is confident his side can progress
The Premier League titleholders took a surprise lead at Old Trafford despite watching Bayern dominate possession, with Nemanja Vidic converting Wayne Rooney's corner after 58 minutes.
Bastian Schweinsteiger equalised for the Bavarians nine minutes later, although Buttner has seen enough to convince him that United are capable of getting a positive result at Allianz Arena.
He told Sky Sports: "Of course we can do it. We always believe in ourselves. We had chances to score more goals and we have to focus on that. Defensively, we did well, we didn't give a lot away, just a goal, and I think we have a good chance.
"It was nice to play. For me it was my first big game and I think I did well. We know they can play good football and for myself I defended well against one of the best wingers. It's good to play a good game."
The left-back also denied that he deliberately handled the ball after Rafinha's blasted effort struck the former Vitesse star's arm.
He added to Dutch TV channel NOS: "I kept my arms together and didn't do it on purpose. I couldn't have done it any other way."
David de Gea, meanwhile, hailed United's support at Old Trafford and Tweeted: "Great atmosphere in Old Trafford!!! Thanks again for your incredible support! You're the best. Look forward to 2nd leg. #MUFC"