The 25-year-old, who has been one of the best players in Europe this season, netted twice as Atletico made it three wins from three matches on their return to Europe's elite competition.
"The plan was to put a lot of pressure on their defenders from the first minute and that was the key. My first goal was beautiful," he told Canal+.
"I always try to take advantage of the fact I'm really fast so I receive the ball and was able to overcome my marker."
Costa, who also recently revealed that he has decided his international future, has scored 10 times in La Liga this season.