Simeone, whose side remain second in La Liga behind Barcelona, backed his side to continue in the same fashion going forward.
"The second-half performance was our best of the season," the coach told reporters after the game. "The team was strong, I knew what I had to do tactically. Sevilla have been doing really well with Vincenzo Montella, but we keep improving.
"[Griezmann] is very good, an extraordinary footballer. Everyone is currently in a brilliant run of form. We played good football and must continue in this way. The system was very well understood by the players.
"We gained a very important victory over Sevilla. [Our next rivals] Leganes will be a tough opponent, as they are strong defensively, but we have to once again play at a high level."
Atletico play Leganes at the Wanda Metropolitano on Wednesday evening.