Emery admitted that Atletico's performance in the first half, in which they scored twice to lead 4-1 on aggregate, was what decided the contest.
"They are having a great season with two players performing brilliantly and the arrivals have been very effective," Atletico's official site quotes Emery as saying.
"In the second half the game was more open but we congratulate them for the way they started the match.
"The first goal was simple but effective and it was over before we found our fluidity."
Sevilla, 12th in La Liga, will now turn their attention to Celta Vigo on Sunday.