Atletico romped to a 5-0 away victory on Saturday, with Kevin Gameiro and Antoine Griezmann both scoring twice after Rober Pier's early own goal.
Those results, along with an away win over Deportivo La Coruna prior to players joining up with their countries, have been crucial in getting Atletico's season back on track after they had won only one of their previous eight.
Despite their mixed start to 2017-18, Atletico have now avoided defeat in all 13 league matches this season, their longest unbeaten run to begin a campaign, and Simeone has been impressed by his side's development.
"We have been growing," he told reporters after the impressive Levante outing, which saw Atleti win at Ciutat de Valencia for the first time since 2007.
"In the last three or four games we have seen improvements in our intensity, pressure and chances.
"The strikers were at their best, especially Griezmann and Gameiro, but [Angel] Correa's work was very good as was [Fernando] Torres'.
"The team is calm and our spirit is being renewed, we don't know why, but it excites us and gives us the positive energy to keep improving.
"The group keeps working, keeps improving. They don't want to stagnate, they keep on pushing. I like that and I'm excited."
13 - Atletico Madrid have recorded their best unbeaten start to a La Liga campaign (W7 D6), surpassing their historic season when they won the double of La Liga and Copa del Rey (first 12 games without a defeat in 1995/96). Optimism. pic.twitter.com/zfJIKMJ4Ae— OptaJose (@OptaJose) November 25, 2017
Atletico and Real Madrid, who also won on Saturday, have cut the gap to the two sides above them in LaLiga, but Simeone was not paying much attention to Sunday's crunch clash between Valencia and Barcelona in the build-up to Atletico's game, something that will not change after the convincing victory.
"We have to win, regardless of whether we are close to one or the other," Simeone said.
"There are still a lot of points to play for and the only thing that occupied me was to win at a stadium I never have."
Gameiro, who ended up with an assist as well as his two goals, added: "We played a great match. We started off well with the goal in the first half. We have to keep it up.
"I'm very happy to have scored. I feel good and I'm going to continue working for my team-mates.
"I have a great relationship with Griezmann and it is good for the team."