Real's win sees them go top of the LaLiga table.
Courtois later said: "We had to dig in during the second half and we found it very tough but we held on, kept going and we did a good job.
"This team knows how to fight and we did just that today. We dug in and defended well as a unit.
"We did concede a few chances but I managed to stop them well. When the rain is coming down like that and you're soaked, your hands and your arms are freezing, but in the end when you're playing a match, the adrenaline is pumping and you focus and forget it."