The Argentina striker hit a hat-trick as Atletico won 3-2 on Wednesday night.
Simeone remarked afterwards: "The team has improved since the Villarreal match.
"We won that game, then in Liverpool, against a huge opponent, we came close to drawing. We also did well in Mallorca. Tonight, in the first half, we could have finished with a bigger lead, but a great goal from outside the box sapped our confidence.
"In the second half, we responded, with some very good moments, even if we lost our way a bit between the 30th and 35th minutes. The 2-2 draw gave us new life, and then the third goal… a real feat."
The undisputed star of the show was Alvarez. Simeone made no secret of the Argentine's importance: "He's the best player we have. We have to protect him and make sure he stays here for many years. Every time he makes a difference, he helps us a lot."
Cholo also emphasised their team spirit: "When we went 2-1 down, we didn't lose our composure or our ideas, and that allowed us to get back into the game. I liked Pubill's introduction; it wasn't easy, and Ruggeri also responded well. These are important signs from someone who starts on the bench."