The visitors, who failed to have a shot in the first half, gained some control early in the second as they played higher up the pitch and pegged their opponents back.
Fernando Torres made his return to the Atleti bench for the first time since he was knocked out against Deportivo La Coruna at the beginning of the month, while Thomas Partey made his first Champions League start.
This is the fourth season in a row that Atletico have made it into the last-eight of the competition, and will be hoping for an extended run.
"That's a demonstration of how well this side defends and how much they do not want to concede".
Bayer Leverkusen are out of the Champions League after a goalless draw with Atletico Madrid in the Spanish capital.
"It was a very open game", Simeone said.
Jan Oblak made one great stop. He was tremendous. He is reaching his best level.
Bayer Leverkusen boss Tayfun Korkut remains undaunted by the prospect of making his Champions League coaching debut in the cauldron of the Vicente Calderon against Atletico Madrid.
Brazil meat scandal: Temer assures foreign markets
According to BBC News, federal police raided 194 locations across six Brazlian states as a part of Operation Weak Flesh. Sao Paulo-based JBS said in a statement that it "vehemently repudiates" claims it sold spoiled food.
Leverkusen was trying to reach the quarterfinals for the first time since it lost to Real Madrid in the 2002 final.
Speaking of the prospect of potentially facing Leicester City in the quarter-finals, Simeone replied: "We are only thinking about the next game against Sevilla". We have no influence in that. "What will be will be".
"Firstly there is joy", said Simeone.
"We know what the situation is with the game after the first leg".
Wendell and Kevin Kample's long-range efforts forced further successive saves from Oblak.
Not 1, not 2, but 3 BIG saves from Oblak! "They didn't have one shot on goal so we kept a clean sheet in the first half", the Atletico keeper continued.
Dermot Corrigan is a Madrid-based football writer who covers La Liga and the Spain national team for ESPN FC.