The key moment in the shootout was a slip by Julian Alvarez, who was deemed to have touched the ball twice by VAR as he converted. As such, the penalty was ruled out.
Simeone said afterwards: "The players who were there today weren't in the previous shootouts. Oblak was, but that's not something to be judged on. We played a very good game, we competed incredibly. We could have increased the score in extra time. Apparently, the referee says he touches the ball, but the ball doesn't move.
"I've never seen VAR review a penalty in a shootout. I'm proud of my players, I'm happy. We couldn't beat them, but they had a bad time... I'm sure they've remembered saying 'these guys always gave us a hard time'.
"We played an incredible game, with a lot of strength and effort. We controlled a team with great players well."
He also said: "The fans left feeling upset, but knowing their team gave it their all. There's a way you can go to sleep thinking, 'Oh, it's bad,' but this team deserved the applause. The fans were there since last night. It was a very nice day, unfortunately we didn't make it. I'm going away, but at peace.
"The way we were eliminated isn't easy to swallow. We have a great opponent on Sunday. Barça certainly wanted us to go to extra time. We're tired, battered, we competed as we should have, but we'll give everything we have."
On Alvarez's penalty, Simeone also stated: "Raise your hand if you see that Julián touched the ball twice! Raise your hand! Nobody raises it!
"I wouldn't talk about luck, I'd talk about feeling proud of the team we have and how to always compete. That will go down in history throughout this entire process we've been through at the club."
He concluded: "Proud of the team we have, our fans must have enjoyed the game. They beat us almost always or always in the Champions League, but they have a hard time, a really hard time."