With the hosts pushing for an equaliser in the closing stages of the game having fallen behind to a Karim Benzema strike, Diego Buonanette went down in the area after a challenge from Casemiro, but the referee waved away all appeals for a penalty.
Mainz was enraged by the decision, but admits he was not surprised to see it go against them.
"The penalty to Buonanotte seems obvious to me," the defender told Goal. "But it's very difficult to get a penalty against Real Madrid with just five minutes to go ...
"The referee didn't see it and we just have to look at the next game against Celta.
"The match was more or less how we expected. We knew we were facing a tough rival but also knew that we would have our chances. Our attitude was great."
The game also generated plenty of debate on account of Carlo Ancelotti's decision to once again select Diego Lopez in goal ahead of club captain Iker Casillas.
The skipper's demotion to the role of an understudy has caused no end of controversy but Mainz said most sides would consider themselves lucky to have such worries.
"That's their problem but, with with the two goalkeepers they have, it's a blessed problem," he added.
