Schwarzer was thrown into the fray after just 18 minutes of the UEFA Champions League clash when Cech landed awkwardly and suffered a shoulder injury which is set to keep him sidelined for the rest of the season.
Australian goalkeeper Schwarzer has had little time on the field this season following his arrival last summer but believes his experience stands him in good stead to handle such situations.
"I'm getting used to this whole thing of sitting out and being ready to play," said the 41-year-old. "It's always a tough thing to do but I didn't really have a chance to think about it, I just went out there and did my job.
"Everyone was up for it, as you'd expect, and we've got world-class players here. We knew that if we could match their determination, our quality would shine through. We didn't create too many chances but I think we did a good job."
Schwarzer helped Chelsea keep a clean sheet as a tight game in Spain ended 0-0, and he is confident they can build on that solid foundation to prevail in the second leg at Stamford Bridge and reach the Champions League final.
Asked if Chelsea were now favourites, Schwarzer told Sky Sports: "I don't think so. It is half-time and it's 0-0.
"We will go into the game at home with the self-belief and confidence that we have done pretty well at home in the Champions League.
"We believe we can play better than we did."
Defender Gary Cahill is expecting Chelsea to adopt a more attacking approach in next week's return leg.
"I don't think you see us sit back in many games there," said Cahill.
"Of course we are going to respect them and they've got some strong players, who caused us problems, but we'll be on the front foot more than we were, I am sure, and we will have a different game plan."