After falling behind to Hakan Calhanoglu's 57th-minute strike, Atletico then had to play the final quarter of an hour at the BayArena with 10 men after midfielder Tiago picked up a second yellow card.
Simeone had also used his three substitutions following first-half injuries to fullback Guilherme Siqueira and midfielder Saul Niguez, and the introduction of forward Fernando Torres, but Leverkusen were unable to build a bigger lead to take into the return leg in Madrid on March 17.
"I don't know if it will be the case but I have the feeling there is life left in us yet," Simeone told a news conference.
"Another opponent, at another time, with us having one player fewer and no substitutions left, would have clinched the tie," added the Argentine. "They did not clinch it and it could give us a chance."
Simeone, who led the Spanish champions to the final of Europe's elite club competition last season, will have to reshuffle his team for Leverkusen's visit to the Calderon as centre back Diego Godin is suspended along with Tiago.
It is unclear whether Siqueira and Saul will be out of action for any length of time, while Simeone is still waiting for the return of Spain midfielder Koke, who has been sidelined with a hamstring problem.
Simeone, whose side play at fifth-placed Sevilla in La Liga on Sunday, said he was confident that his squad had enough depth to cope with the suspensions and mounting injuries.
"The absences will be covered by players who have been training, preparing and who are part of a competitive squad which knows they depend on the group as a whole to cope with these situations," Simeone said.
"A team can win one game but a squad can help you achieve important things.
"Let's see if we can do it with the lads coming in whose turn it is to play."
(Writing by Iain Rogers, editing by Peter Rutherford)
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