Neuer returned to Bayern's team on Friday, following a three-game absence due to a thumb injury, but conceded after just 13 seconds in the 3-2 Bundesliga win over Augsburg when Leon Goretzka deflected into his own net.
It was the fastest own goal in Bundesliga history, leaving the club with an early hill to climb.
David Alaba's second-half goal proved the winner for the German giants, who closed the gap on league leaders Dortmund to just two points, though their rivals will hold a game in hand until they take the pitch on Monday against Nuremberg.
But Neuer was not pleased with how his club played at the back and says Bayern must cut out on the "madness", especially if they are to come away with anything from the first leg of their Champions League last-16 clash with Jurgen Klopp's side at Anfield on Tuesday.
"The game was all great, but conceding the goals was, of course, madness," Neuer told reporters. "You cannot do that.
"We wanted to keep a clean sheet again, the good thing was that we still had time after the 1-0.
"Liverpool will have more chances to score. We were caught cold twice on the wings, we need to stand better, occupy the box better and organise ourselves very well, especially with passes over the side so we can prevent that."
While Neuer was annoyed, manager Niko Kovac floated the belief that his side might have been overlooking their opponent on the day with a clash against the Premier League side looming.
The injury to Coman will also come as a blow as the club enter a busy time, with matches against top half clubs Hertha, Borussia Monchengladbach and Wolfsburg all on tap between the first leg against Liverpool on Tuesday and the return leg on March 13.