Atletico's UEFA Champions League campaign got off to a disappointing start in September, beaten 3-2 at Olympiacos in their opening Group A fixture.
But the La Liga champions - runners-up in the Champions League last season - exacted revenge by routing Olympiacos 4-0 at the Vicente Calderon as they qualified for the knockout phase.
A Mario Mandzukic hat-trick and Raul Garcia's ninth-minute opener saw Atletico to their fourth consecutive continental win.
"We have produced some good performances recently," Simeone said post-game.
"Tonight we had continuity in our game and we were focused on the areas where we could hurt them.
"Intensity is the key for this team. After a tough beginning [with the defeat at Olympiacos] it has been a great effort from my players to take us to the next round."
Simeone was reluctant to single out hat-trick hero Mandzukic, though he did praise the impact made by Atletico's new recruits.
Mandzukic, Miguel Moya, Cristian Ansaldi, Antoine Griezmann and Raul Jimenez all featured against the Greek champions.
"That affirms the work of this squad and how the team have been reinvented with ten new players to keep on being competitive," Simeone said.
"There are many games to play and the most important thing is the quality of the minutes every player plays. Many players are in good shape and it's not easy to be in the starting line-up."
