Leverkusen could only manage a goalless draw at the Vincente Calderon on Wednesday as Atletico advanced to the quarter-finals 4-2 on aggregate.
Leno and his team-mates were left ruing their efforts in the opening leg last month, which left them with too great a hurdle to overcome.
However, goalkeeper Leno - who made two fine saves to deny Angel Correa and Koke in the first half - said Leverkusen could walk away with their heads held high.
"Luck wasn't on our side. [Atletico keeper Jan] Oblak had to make three really good saves," Leno said via UEFA.com.
"It was still a really good performance from us - and definitely a step in the right direction. We damaged our chances of progressing with our performance in the first leg.
"We proved that we're capable of matching teams like Atletico if we play to our potential. We can be proud of our performance this evening."
While chances were few and far between in the Spanish capital, the scoreline could have been different had it not been for Oblak, who produced a stunning triple-save to keep the scores level on the night.
"We had three great chances in the second half. Had they gone in, we might have had a chance of progressing," Leverkusen forward Kevin Volland said.
"It's just a shame we lost the first leg so heavily, but the goalless draw here gives us confidence."