Griezmann has endured a slow start to his career in the Spanish capital since joining the Liga champions from Real Sociedad during the close-season.
But the France international opened his league account for his new club with a brace on Saturday, before Mario Mandzukic and substitute Raul Garcia closed out a win that moves Diego Simeone's team on to 23 points and firmly into the congested early title race.
"I knew I had to change some things when I came here and so I'm doing everything to do that," Griezmann was quoted as saying by AS.
"We always give everything at the [Vicente] Calderon and the supporters help us reach a higher level.
"The most important thing is I'm getting to know my team-mates and they're getting to know me.
"We remain on the right track. I'm happy for the victory and for the goals I scored."
Speaking at his post-match press conference, Atletico coach Diego Simeone praised his new-look team's intensity in the face of a spirited challenge from Cordoba, who got on the scoresheet through Nabil Ghilas' double
"It was a great match," he said.
"The team improved, we continue to grow. We kept the intensity in the game."
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