Atletico went 2-0 ahead on the night and 4-1 on aggregate before Sevilla pulled two goals back. The visitors managed to hang on to go through.
Simeone said that the club are delighted to have reached the final but that they will now turn their attention to the La Liga clash with Malaga.
"We showed a very good attitude from the start," Simeone told the club's official website. "Early on in the match I saw a team that had the ambition to reach the final.
"Then came the goals and that made it easier to see the game out. We got the goals but then found it difficult against a very brave response.
"We are enjoying that we have reached the final, but tomorrow we will focus on Malaga, which will be a difficult challenge."
Atletico are currently second in La Liga, four points ahead of city rivals Real Madrid.