A 4-1 win over Club Brugge on Tuesday night saw them win their playoff 7-4 on aggregate.
Asked about his celebrations at the final whistle, Simeone said: "Because I'm very happy. There's a huge amount of work behind these results, which are starting to be more positive than negative. Many players have come in over the last two seasons, and reinventing ourselves isn't easy.
"When you see the substitutes come on... I still get emotional. When I see that commitment, I feel a strong connection. I'm very proud of the guys. We came up against a team that plays well, that eliminated Atlanta last year... We were better in the second half."
Simeone also said, "They were attacking to win the game, and we were playing like I don't know what. We had to change our approach, increase the intensity of our pressing, be more decisive in our attacking work... Cardoso's goal helped us, and the substitutions did too. It wasn't easy to leave Griezmann and Lookman out, but seeing the players who came on like this is exciting. It wasn't an easy decision."
Alexander Sorloth hit a hat-trick on the night and the coach added: "We had the same problem with Griezmann last season; we kept playing him and he couldn't create anything. I believe in these players, they're very good.
"And Sorloth is playing today because he did very well against Club Brugge. The way he came on for those 20 minutes in Bruges, the chances he had. I hope he can continue like this because he's very important for the team."