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.
"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.
