The Bundesliga outfit have not been past the last 16 of Europe's elite club competition since reaching the final in 2001-02, but moved a step closer on Wednesday.
Hakan Calhanoglu's second-half goal separated the two sides at the BayArena, while goalkeeper Bernd Leno kept Atletico at bay on their few attacks.
Victory leaves Schmidt's side needing to avoid defeat in Spain to book their place in the next round.
"You could tell how much we looked forward to playing Champions League today," said Schmidt.
"We take this competition very seriously.
"It was a first step and it would be a dream if we could reach the quarter-finals.
"We defended well, were compact and always in a position to help each other. We also made good attacking transitions and were very direct going forward."
Leverkusen travel to the Vicente Calderon – where Atletico have not lost in the Champions League since December 2009 – on March 17.
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