Courtois was named man of the match for the 3-1 Champions League win.
He later said: “Stuttgart are a very offensive team and play well, but they also leave space at the back. In the first 25 minutes, they hurt us, but then we improved and scored a goal. Then we failed to take advantage of counter-attacks and quick transitions, but we reacted well to their goal and we got the win.
“They pressed well. Sometimes we came out okay and other times we made things difficult for ourselves because we couldn't see the free man. It's something we have to work on. It's very important to start with a win in this new Champions League format.
“There was a lot of space at the back and that's how the first goal came. That's where the game was going and we didn't make the most of it.”
Courtois also gave his shirt away to one young fan after the final whistle.
He added, “There was a boy with a goalkeeper's shirt and a nice banner. There aren't many who come with a goalkeeper's shirt in the stadium and I hope that by giving him this shirt he can fulfil his dreams. You never know if he might make it (to play in) this goal.”