Midfielder Saul started the clash on the bench, but he was swiftly called upon when Koke was forced off with a hamstring injury and left his mark on the encounter with a stunning overhead kick to double Atletico's lead after Tiago had opened the scoring.
Antoine Griezmann and Mario Mandzukic completed Real's humiliation in the second half and Simeone was elated with his team's complete performance, though he reserved special praise for Saul and left-back Siqueira.
"The players are the most important thing," he told reporters. "They carried out the match to perfection.
"We attacked down the right and defended with Tiago and Gabi. Koke's injury was a blow, but Saul was brilliant. He played very well. He's very important for the future.
"He knows it and the club knows it. That's why I wanted him to stay. But he needs to be patient.
"We need his rebellious streak and his youth, but also his patience. Koke and [Jose Maria] Gimenez were the same.
"That was possibly his best game," Simeone added about Siqueira.
"He was solid at the back, good attacking. He provided an assist, he covered well and he knew when to press.
"He's a very good kid and he's worked hard at this. That's why he has improved, the same as Griezmann."
Simeone also acknowledged the impact of the fans on Saturday's triumph, thanking them for a rapturous ovation at the end of the match.
"We have to thank the players for the afternoon we had," he added.
"It was a really great one, where the team played well, being really convincing and serious. And that is something to be grateful about, and the supporters were indeed.
"It was lovely when they sang 'proud of my players', something not often heard in other stadiums. Hopefully, we can continue like this."
