Neuer said words just could not describe their disappointment.
"Defeats always hurt, but this is a moment in which we feel empty," he said.
"We really don't know how this could have happened in such a way. We just lacked that tiny bit of luck. I am just lost for words.
"We always believed we could keep the cup here and we were always on top of this game, whether in normal time when we went 1-0 up, or in extra-time despite the penalty miss, we were just generally the better team over 120 minutes.
"Then to be ahead in the penalty shoot-out, with everything running for us, we had one hand on the cup. That is why it hurts so much.
"Now we are left wondering when we are going to have a chance to play in a Champions League final again."