Atletico prevailed 3-2 on penalties after the match finished 1-1 on aggregate following extra-time at the Vicente Calderon, with Mario Suarez’s 27th minute goal giving the Spanish champions a 1-0 win on the night.
Stefan Kiessling missed the decisive spot-kick for Leverkusen, but Schmidt placed no blame on his players.
“A penalty shoot-out always has something to do with nerves,” he said in Kicker. “Therefore you have to have a bit of experience. Playing in your own stadium is also easier if you are cheered instead of being booed.
“But that we ever made it to a penalty shoot-out is a remarkable achievement. It is a pity the team has not been rewarded. We put up a very, very big fight.”
Sporting director Rudi Voller added: “There is no use criticising anyone. We have to keep our heads up. When you lose in a penalty shoot-out, it is very, very bitter. This is of course a lottery.”