Oblak produced a remarkable triple save midway through the second half as Atletico held on to their 4-2 first-leg advantage to take their place in Friday's draw for the last eight.
"It is not easy to be in the quarter-finals four years in a row," Oblak told BeIN Sports Spain.
"I hope Atletico will continue like this, keep growing like in the last few years and I am sure we can achieve great things."
Two weeks on from being knocked unconscious in a sickening head clash Atletico boss Diego Simeone left Torres on the bench for the full 90 minutes.
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New Leverkusen boss Tayfun Korkut was taking charge of his first Champions League game after Roger Schmidt was sacked when Leverkusen's first-leg defeat was followed by a 6-2 thrashing at Borussia Dortmund.
Korkut summoned a much-improved performance from the Germans as they forced Atletico onto the back foot for long spells.
However, the damage had already been done as the hosts registered their 17th clean sheet in their last 21 Champions League home games.
Atletico have only ever been eliminated from the Champions League under Simeone by Real Madrid.
Javier Hernandez got Real's winner in their quarter-final clash two years ago, but the Mexican didn't come back to haunt Simeone's men as he blazed over with another decent opening.
Atletico took until seven minutes before the break to threaten but then forced Bernd Leno into two fine saves in 60 seconds.
Firstly, Angel Correa was denied before Koke's low driven shot was turned behind by the German international.
At the other end, Atletico went close twice in quick succession once more as Correa danced inside two Leverkusen challenges before stabbing just wide.
Antoine Griezmann was then inches away from his 22nd goal of the season with a measured chip over Leno that floated just wide.
The highlight of the match came 21 minutes from time when Oblak pulled off an incredible triple save to end Leverkusen's hopes of a comeback.
Brandt pounced on a slack pass from Jose Maria Gimenez and after he was denied one-on-one with Oblak, the Slovenian twice pulled himself off the ground to save Volland's follow-up efforts.