The Primera Division team were held to a 1-1 draw by Leicester City at the King Power Stadium on Tuesday but advanced after winning the first leg 1-0. Antoine Griezmann had scored the only goal in that game, from the penalty spot.
Saul Niguez opened the scoring for Atletico this time around ahead of a Jamie Vardy equaliser, that ensured a tense final half an hour for Simeone's charges.
Speaking after the game, the Argentine boss said: "I'm full of emotions, full of pride for the performance of my team. Full of hope and excitement as we progress.
"But I have to say what a great performance from Leicester, it was almost a pleasure to compete against them. We were living in fear all night of what they might achieve. They pushed us all the way.
We performed in the way this match needed us to perform. We always come up with a solution. I don't like to praise too much but we responded and played in the we needed to."
Atletico have been beaten finalists in two of the last three years, but Simeone says that just means they are on the right track.
He added: "It is great to be in the semi-finals for the third time in four years. Looking back at the first day I arrived at the club, I said my desire was to make Atletico Madrid competitive against every team we played against. It is satisfying now to say we are a competitive outfit."