Barca won 2-1 at the Metropolitano, with Eric Garcia seeing red, but lost the quarterfinal tie 3-2 on aggregate.
Simeone declared afterwards: "Did you see how they play? The speed they go at? We made some important mistakes that allowed them to capitalize with all their passing and combination play, and it became difficult for us to control.
"But at 2-0, the game could have slipped away, and we could have given up. We played back and gotten back up. And we did, thanks to the personality of Giménez, Koke, and Llorente, the composure of Musso, Giuliano started to improve, Lookman brought us back into the game... In the second half, it was more even.
"We knew Barcelona would tire after their effort on Saturday, and our substitutions gave us energy. We both brought out our Plan B: them with Araujo and Lewandowski, us with Sorloth, Nico, Baena... They came close to scoring, and so did we."
He added, "It was an extraordinary match that we started winning thanks to the fans we saw from the bus on the way to the stadium. It's been 14 years, and I still get emotional. I thanked the players for their faith, heart, and drive. Now it's time to rest for what's next."
Ademola Lookman struck the crucial goal for Atletico and Simeone also said: "He continues to evolve completely, improving tremendously defensively, with a greater impact on the team. He has everything offensively; we've never had players of that caliber.
"We're committed to playing with four forwards, even though some say Giuliano is an attacking midfielder or full-back. Lookman is breathtaking; he has so much more to offer. I saw it with Nigeria, and that's what I want from him."
Asked about winning the Champions League, Simeone said: "With the enthusiasm of the three remaining matches, with respect and humility, but knowing what we want. And we will go for it."