The Bundesliga outfit appeared to need a minor miracle as they attempted to turn around a four-goal deficit from the first leg in the return fixture on Wednesday, although they were boosted when Sidney Sam opened the scoring after just six minutes.
However, it all went wrong from there for Hyypia's side, who conceded an equaliser to Marquinhos before captain Simon Rolfes saw his penalty saved before the break.
Despite the Germans threatening throughout, Ezequiel Lavezzi then scored the winner eight minutes after the break for the French champions, with Leverkusen finishing the last 16 clash a man down as Emre Can was sent off for a second bookable offence.
However, Hyypia was proud of his side's display in the 2-1 reverse, saying: "I hope everyone saw that we delivered a good performance today. I am quite happy with the attitude that my team showed.
"Overall, I feel we can leave here with our heads high. Coming into today, nobody believed in us. But I am glad we showed that we can perform."
Rolfes added: "It is not easy playing when you know you are out, but for us it was about honour and prestige.
"At least we managed to keep the game open a bit longer than last time, but after the red card it was not possible to put them under pressure."
