The Blues headed into the second leg needing to overturn a 1-0 deficit but goals from Juan Mata, John Terry and Fernando Torres sealed progression despite a Vlad Chiriches strike on the stroke of half-time.
Though admitting that his side made things difficult for themselves, Cech argues that Chelsea drew strength from their revival from 2-0 down against Manchester United in the FA Cup on Sunday.
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"It was a big win because we wanted to qualify for the next round. This wasn't the stage we wanted to go out of the competition."
The goalkeeper also praised the performance of Torres, who scored Chelsea's third and decisive goal but missed a penalty just minutes later.
"I think he was working hard and he took his chance well," Cech observed of the Spanish striker. "It was a pity for him the penalty didn't go in but it was important we got the win."
Now the 30-year-old insists that every Chelsea fixture will be treated like a "final" as the London club, who are currently fourth in the Premier League, continue to fight on three fronts in the closing stages of the season.
He added: "Every game is a final for us because we are chasing third spot in the league and we are in the Europa League and the FA Cup. We have a lot of games and it's not easy at times but we'll keep fighting."