Real won 1-0 thanks to Toni Kroos' goal, with Courtois making three exceptional saves.
Courtois said, "Tonight's was an important match, we had to win to get some breathing space in order to stay alive in the Champions League. It's a stadium with a big atmosphere and they really get behind their team. We were in the match from the start, although they had two big chances at the beginning that I saved well. In the second half we controlled the match more, but we failed to kill the game off.
"Everyone was really up for it and that's the sort of intensity we have to produce in every game to win. We had chances that could have ended up in goals, we didn't manage to score a second, but are happy to have got the win, although we need to improve on that. We're going to keep on working and let's hope we win more games."
He added: "I never doubt myself, but we know just what a club we're at and I'm only interested in constructive criticism from my teammates and the coach. I'll keep on training hard to keep performing to this standard."