The Atletico Madrid coach accepted the 2-1 aggregate defeat with characteristic dignity while deliberately avoiding the penalty controversy that threatened to overshadow the tie.
Simeone was shown a yellow card in the closing moments after shoving Arsenal sporting director Andrea Berta as tensions boiled over near the technical areas. He made no reference to the incident in his post-match press conference, focusing instead on his players and on the scope of Atlético's achievement this season.
"If we are knocked out it is because the opponent has earned it — starting with being decisive in the first half. I feel calm, peace, knowing the team gave absolutely everything they have."
He acknowledged Arsenal's clinical edge made the difference across both legs.
"We could have won the first match, but we weren't as decisive as we needed to be. Today we improved defensively in the first half but offered little offensively. In the second half we improved and there were situations that didn't go in our favour."
On the question of the penalty that Atlético felt should have been awarded for a foul on Antoine Griezmann, Simeone was deliberately brief.
"I'm not going to focus on something as simple as the Griezmann incident. We thought there was a foul on Pubill. But I don't want to hide behind anything."
He expressed admiration for Mikel Arteta, who guided Arsenal through what would have been a daunting final 20 minutes.
"Arteta's work is very good and he has financial power that accompanies it. I am pleased for them — they have been trying for years and the work pays off."
Simeone paid particular tribute to Griezmann, who may have played his final Champions League match at Atlético, and captain Koke, who also came off the bench as the club's all-time appearance record holder.
"Total gratitude. We competed with Barcelona and Arsenal incredibly through the effort of these players. With Antoine, I hope the fans give back the effort he has given over the years. And what Koke has been is extraordinary."
He closed with a broader reflection on Atlético's place in the modern European game.
"It gives me a reality — which is what Atlético is as a club. It has grown enormously and is now recognised across Europe and the world as it wasn't before. But the fans want to win. Reaching a final is not enough for them — and we are the first ones who want that too."