The 2014 beaten finalists suffered their first loss since the opening group game of the competition as Hakan Calhanoglu gave Leverkusen a narrow advantage at the BayArena.
Having scored 14 goals in the group stages, it was a frustrating night for Atleti, with Bernd Leno in good form to keep out the few chances the visitors were able to create.
Atletico now have to score at least twice in the return leg, however they will be confident given their last defeat at the Vicente Calderon in this competition came in December 2009.
"It was a difficult game," said Atleti's captain. "They were intense and pressed a lot.
"They were up for it and that's what defeat us. But the second leg is still there and we will try our best to turn things around.
"We had a few chances, but we couldn't grab a goal. They deserved their win.
"It's hard to take but I am confident we can go through."
Diego Simeone's side will be without midfielder Tiago for the home leg of the tie, though, after he received a second yellow card with 14 minutes remaining.
