The Blues produced a dogged defensive performance in the Champions League semi-final first leg at the Estadio Vicente Calderon which sets up an intriguing second leg battle at Stamford Bridge next week.
Australian veteran Schwarzer was able to deny the Spanish league leaders after replacing Petr Cech in the 18th minute after the Czech international was forced off with a dislocated shoulder.
Schwarzer, who played a full 90 minutes in Chelsea's 2-1 Premier League loss to Sunderland on the weekend, felt the London club did a decent job in denying Diego Simeone's Los Rojiblancos as they now look forward to the top-of-the-table domestic meeting with Liverpool at Anfield on Sunday.
"I think everyone was right up for it, as you would expect," the former Fulham and Socceroos star told ITV Sport after the match.
"We have world-class players in the side and we didn't expect anything less.
"We knew if we could match their determination, that our quality could come through.
"Okay, we didn't create too many chances, but we did a good job tonight."
Schwarzer added: "It is very tough, but you have to take each game as it comes.
"We now have to think about a massive game on Sunday (against Liverpool in the league), and then it's the return leg."
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