Real won their Champions League clash 2-0 thanks to late goals from Fede Valverde and Marco Asensio.
Courtois said, "That's a good team we've beaten and they made us work really hard for the win.
"Really we didn't play well in the first half and the state of the playing surface didn't help us establish our game as we wished.
"During half time the coach told us specific things he wanted to change and improved. After that we began to play better.
"Maybe when we played better we still didn't make huge danger but the key was that we took our chances. It was important to start our defence with two-straight wins. Now if we can win our two against Shakhtar we'll be nearly through to the next round."