Courtois kept a clean as Real Madrid won 1-0 on Wednesday night, with Jude Bellingham scoring the winner.
The Belgium international said afterwards: "I'm delighted with the win. I'm really happy, it's nice to mark my 300th Real Madrid appearance with a 1-0 win, a decent performance and some good saves. I think my best stop today was the one-on-one with Vlahović. It was really good from a technical point of view.
"It was a really hard-fought game with chances at both ends. We really had to sweat to win it. It's a big win, especially against another great side. That's 9 from 9 now. Next up we head to Anfield, so we'll see what happens. We've started well and we just have to keep working hard."
On Bellingham's goal, Courtois added: “That's what I like about those kinds of players. Vini Jr. made the move and he was alert to the rebound, he knew it could fall where he was placed.
"He's rediscovering his best form. It was a great performance by Jude, and by the whole team. We could have done with that 2-0 so we could be a bit more relaxed, but we're happy with the result in the end."