Borussia Dortmund exacted a degree of revenge for their UEFA Champions League disappointment at the hands of Bayern back in May by running out 4-2 victors at Signal Iduna Park to take the trophy.
Strikes from Marco Reus, Ilkay Gundogan and Pierre-Emerick Aubameyang allied to a Daniel van Buyten own goal secured the win, inflicting defeat on Pep Guardiola in his first competitive game in charge in the process.
But Mueller believes that the result simply underlines the need for his team to continue improving under the guidance of their new boss.
"It clearly means we were doing something wrong. I'll need to take another good look at the whole thing," he said.
"On the positive side we didn't let up, just as we hadn't after going 1-0 behind. After being 3-1 down we came back again - I nearly made it three-all myself. If that had gone in, the game might have taken a different course altogether.
"Instead, we pressed forward, got caught on the break and conceded a fourth goal. I can live with that, but we really needed to hold our shape better, especially when it was 1-1. I'm not pointing the finger at anyone, but it's not good enough."
The Germany international stopped short of proclaiming his team's season dead and buried, however, insisting the result is one Bayern can easily recover from.
"Which game ever implies anything about the future? Any match can take a turn for the unexpected, however well or otherwise things have been going beforehand," he added.
"On top of that, we didn't play badly against Dortmund. We just weren't good enough to win the game on the night.
"Up until the Super Cup, our preparations were going really well, also in terms of the results. But any team can be beaten if they don't perform at their best, ourselves included.
"And that applies even more when you're playing Dortmund, who are a great team as well. If you take last season's Champions League as the form guide, they're the second-best side in Europe.
"So we didn't lose the Super Cup to any old team. Although that said, we'd still rather have won it!"
Bayern won an unprecedented Bundesliga, DFB-Pokal and Champions League treble last term under the tutelage of Jupp Heynckes.
