The Colchoneros booked their place in the final of the competition with a 2-2 draw, running out 4-3 winners on aggregate.
Costa was at the centre of the red-card controversy after Gary Medel and Geoffrey Kondogbia were both dismissed in separate incidents involving the Brazilian.
But he told reporters after the game: “They did not go out to get to me, it is just that I was there.
“I had everything under control. I was down on the ground and was not going to get up [after Kondogbia’s challenge].”
After the match, Atletico manager Diego Simeone said he believed his side had fought hard for the win.
“I found that the team gave it everything, they looked for the goal and found it and it became more difficult for the opponents to play.”
Two early goals from the visitors left an almost impossible obstacle for Los Rojiblancos, but midfielder Jesus Navas believed his side showed what they were made of and continued to press.
“Their two goals came too soon, especially the second, because then we had to score four.
"But the team did not give up, we persisted and pulled level with one man less.”
Goalkeeper Unai Emery added: “The team remained motivated, but the first goal was scored by them after a basic move, basic but effective.
“We conceded a goal that generated big questions that we must react quickly to. There were moments, but we still could not score that goal [we needed]."