The Rojiblancos, who have never previously reached the final of the competition, set up an all-Madrid showdown in Lisbon by winning 3-1 at Stamford Bridge last night.
"We did everything within our power to get through to the final and we deserve to be there, as do Real Madrid," Simeone is quoted as saying by Sky Sports News. "Fernando Torres got the opener but we knew that one of our goals would count for double and so we had to fight to score it.
"We had to work so hard in order to find ourselves playing the type of game that suited us, which came from the second goal onwards. Tonight was the result of a big collective effort. We generated that possibility of us reaching a beautiful final.
"It was a smashing game in the first half, tactically speaking, until the first goal opened it up. They had the first chance but we managed to equalise relatively soon afterwards."
Atletico return to league action on Sunday with a visit to face Levante.