The abrasive front-man led the line in the semi-final first leg against Sevilla at the Calderon, when leading scorer Falcao was out injured, and scored two penalties to help Atletico to a 2-1 victory.
In the return leg in Seville on Wednesday, he carved out the first goal for himself and set up the second for Falcao inside the opening 29 minutes, and the side held on for a 2-2 draw to progress 4-3 on aggregate.
Costa's seven goals in the cup make him the top scorer in the tournament to date.
"These things happen in football. We know Costa is provocative and we fell for it," Sevilla captain Negredo said after the game.
"When you lose you feel this impotence," Simeone told a news conference. "A striker with Costa's characteristics is difficult to mark, and the episodes at the end are part of the game."
"I had it all controlled," he told reporters. "They didn't come looking for me, I just happened to be there. When I dished it out people used to call me an assassin. I know I have made mistakes, but I try to control myself more now.
"The team are playing well and this is the reason why I am doing well," he added. "I don't consider myself a leading figure and will carry on working hard to try and improve."
"After the game we shook hands and there were no problems," Costa said of the last derby.
