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The reigning champions secured the victory at the Allianz Arena thanks to a stylish volley from Muller early in the second half and Leon Goretzka's deft finish late on.
However, Hansi Flick's men were far from their fluent best against an Augsburg side who stifled their hosts' attacking threat and had chances of their own.
"We have missed the killer mentality," Muller told Sky Sport in Germany. "That coldness that has characterised us in the past few weeks.
"This is not the feeling we want to have.
"We played the more compelling football and had significantly more chances. But goalkeeper Manuel Neuer we owe thanks for it not being 1-1 in the 85th minute.
"Of course, we are complaining after playing a very high level. It's a matter of getting us back on track physically and mentally. We have to take a deep breath this week and give it another push."
Head coach Flick agreed Bayern's performance was not up to their usual standards and was relieved they came away with the three points.
Bayern have a four-point lead over second-placed Borussia Dortmund at the top of the Bundesliga table.
"We knew it would be a difficult game," added Flick, who has a contract at Bayern until the end of the season having replaced Niko Kovac.
"The first half in particular showed that. Augsburg sat deep and closed the space.
"In the second half we took the lead but we then failed to close the game earlier, and Augsburg had a huge chance to equalise.
"The 2-0 was a relief for us. The bottom line remains the three points, we wanted that and we got it."
Bayern are now on a six-game winning run and have not lost since December 7, when they went 2-1 down to Borussia Monchengladbach.