The attacker was pleased to have a chance to impact on the game despite not being the starting XI and Manuel Neuer discussed how he saved Mesut Ozil's penalty.
Both sides missed penalties in the first half, with Mesut Ozil and David Alaba the guilty parties, while Gunners' keeper Wojciech Szcezny was sent off for bringing down Robben for the Bavarians' spot kick.
Toni Kroos eventually broke the deadlock with a stunning curling effort from the edge of the box early in the second period and Muller then came off the bench to score a killer second and put his side firmly in control of the last 16 tie Champions League tie ahead of the second leg in Munich.
"I was not surprised at not starting," the Germany international, 24, told Sky. "Pep and I talk to each other so I knew what was coming. Of course I am not happy with it. But he knows and is aware that I am a total team player. A match lasts longer than 60 minutes and I am happy I could come in and help the team."
Manuel Neuer saved a penalty from Mesut Ozil in the opening 10 minutes to stem what was a strong Gunners start, but says his years at Schalke with the midfielder did not mean he knew where he would shoot.
"No, the most important thing is how he runs towards the ball," the Bayern goalkeeper said. "He is a player who decides very late where to shoot. So I waited long enough so I could save the ball even if it was placed in the middle."
The Bavarians will host Arsene Wenger's men at the Allianz Arena on March 11 in the return leg.