Vinicius Jr scored a hat-trick, with Antonio Rudiger and Lucas Vazquez also scoring. All Real's goals came in the second-half after Donyell Malen and Jamie Gittens had BVB 2-0 ahead at the break.
Courtois later said: “We didn't play well in the first half, they caused us all kinds of problems and scored two really quick goals. We tightened up after the break and discussed what we had to improve. We reacted well and we knew that if we could get that first goal, we could win it. In the second half, we pressed better, played really well and showed the intensity required of a Champions League game. That was the difference.
“They were finding it really easy to play against us and it could have been 3-0 at half-time. We woke up and reacted well but that's not always going to work. On Saturday we have to start the game like we finished today.
“On the pitch you can really feel that the opposition know they're up against Real Madrid. I'm not saying it's fear but when you score, the atmosphere in the stadium heats up and the opposition feels that. At 2-2 it was about playing it calm and bringing some organisation. Then we were able to get another three goals. If we play like we did in the second half, Saturday will be a better display."