The Premier League side went 1-0 down at the Santiago Bernabeu, but did not lose their nerve.
They turned around the game and won 2-1 on the night, while Real defender Sergio Ramos was sent off.
Midfielder De Bruyne told the club website after the game: "It's a very good start.
"We struggled in the first 15 minutes but you have to go through the storm.
"It was an even first half. We started the second half really well. Their goal came at a bad moment for us - we were dominating. Our response was brilliant. It was a beautiful goal from Gabriel Jesus.
"In four years with Pep, he sometimes surprises. Sometimes players aren't told until the game what we need to do. There were some good and some lesser moments. In a quality game like this, you'll struggle sometimes.
"We're only halfway there. We have an important game at home in three weeks. Now we have to recover for Sunday's final [in the Carabao Cup against Aston Villa]."