The 23-year-old knows that his team must improve if they are to have any hopes of repeating last season's treble-winning success, having been beaten by Borussia Dortmund
The Bavarians were favourites to retain the trophy, going into the game on the back of a fine pre-season, but Jurgen Klopp's side responded and ran out deserving winners.
"We were pretty disorganised after equalising - and that lasted a few minutes after we conceded the two goals, as well," the 23-year-old told reporters. "I noticed that everyone seemed to be occupying a different position. After that, we managed to regain our structure.
"When push came to shove and it mattered most, we weren't able to do the things that would have won us the match.
"It clearly means we were doing something wrong. I'll need to take another good look at the whole thing. 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. 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."
Despite the outcome, Muller is confident that the game was a one-off result and believes that the club will be fine moving forward.
"Which game ever implies anything about the future?" he mused. "Any match can take a turn for the unexpected, however well things have been going beforehand. 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 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 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!"