Real won 3-0 thanks to goals from Kylian Mbappe (2) and Vini Jr, with Courtois keeping a clean sheet.
The Belgian told Real Madrid TV afterwards: "It's a very important victory. Winning away from home with a clean sheet is important. The level we were at, the reactions, the pressure, they were very good until the final whistle. We knew it was a tough match, it's the first one against Oviedo in the Primera for 24 years.
"It's a Primera División stadium, a Primera División team and I loved playing here. We knew it was going to be tough, they did well at the start, but then we bounced back and created a lot of danger. Their goalkeeper did a great job to keep the game very even until the end.
"In attack, we could have finished the game off earlier. At 0-1 you know that they can always have moments, like the one that hit the post. All 11 of us defended very well, we pressed well and that's how we're going to win a lot of games. In attack, at the end we had 10 shots on goal and three goals, so it's important."
Xabi wants me to run!
Of his own form, Courtois smiled: "I feel good. In the end, against Osasuna I didn't have much work to do. The coach (Xabi Alonso) is asking me to play much more forward, so I'm running a lot. I'm accompanying the team because when they press high up the pitch I have to stay there; I'm often in the middle of the pitch.
"It's about staying focused, like that save at the end, and keeping a clean sheet. The match was about keeping a clean sheet for everyone and in the end winning 0-3 is better than 1-2 and enduring the last few minutes."