Muller: Bayern Munich in no position to complain
Thiago Alcantara got the decisive goal for Bayern, as the Bundesliga champions made it three wins from three in all competitions to ease the pressure on Niko Kovac.
Leon Goretzka had volleyed the visitors ahead, but Jean-Paul Boetius responded for Mainz after the restart after a lapse in concentration from Bayern's defence.
And although acknowledging Bayern have many areas in which they must improve, Muller insists they cannot be fussy over how they pick up points.
"Mainz often make it difficult when they are at home," Muller told Bayern's official website.
"Nevertheless, we had a lot more chances to score. We can live with the 2-1, it's not like we're flying through the league and the games right now.
"We wanted to win by more than one goal, but we are not in the position to complain about victories at the moment.
"We set the tone and had to score more in the first half. After the break we fell asleep but we came back well."
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Despite their troubles, Bayern are now just two points behind Bundesliga leaders Borussia Dortmund, who were held to a 2-2 draw by Hertha Berlin, and although Kovac echoed Muller's thoughts, the coach was satisfied with a deserved win.
"It was a hard win, which was certainly not as good as we had hoped," Kovac said.
"But in our current situation, we are happy to have won our last three games. I think the victory was deserved. We are satisfied and we hope it will continue.
"I was annoyed that what we had discussed during the break was not implemented. We fall asleep and get into trouble. But I'm glad that the team still created opportunities."