David Alaba and Arturo Vidal had chances cleared off the line in quick succession, while Kingsley Coman and substitute Philipp Lahm failed to make the most of chances around the six-yard box.
Lahm's effort came after Leverkusen had been reduced to 10 men, Tin Jedvaj shown a second yellow card in the 59th minute.
Muller was also culpable for Bayern's inefficiency in front of goal, proving indecisive when presented with a chance to shoot from the right-hand side of the box.
"Our play and attitude were good, but the missed chances were fatal and if you do not score a goal you cannot win," said the forward, who played in place of suspended top scorer Robert Lewandowski.
"We had three, four, five clear chances. I had a really good opportunity to score but I made the wrong decision.
"That's why we are mad at ourselves."
Alaba was similarly frustrated, but he tried to remain upbeat ahead of Tuesday's trip to the Santiago Bernabeu, where Bayern will look to overturn a 2-1 deficit against Real Madrid in the Champions League quarter-finals.
"The positive thing is that we have made a lot of chances, but we unfortunately haven't been able to take them," said the Austria international.
"In the end you have to score the goals to leave the pitch as the winner.
"Now we have a few days. We believe in ourselves. We are very motivated and look forward to the game in Madrid.
"We will give all we have in order to be successful."