Villa joined Atleti from Barcelona in July for €5.1million and scored his first goal for the club by grabbing the opener in their 2-0 win over Segunda Division outfit Deportiva Las Palmas on Saturday.
"For a striker the most important thing is to score goals and it is important scoring a goal on your debut," Villa told reporters.
"I am very happy because we worked hard this pre-season.
The 31-year-old then revealed he is adapting well to a new style of play under Diego Simeone and explained how he had done additional fitness work to get up to speed with his new team-mates.
"After the training all this week I am getting better and I'm very happy and very pleased that everything is going well," he said.
"Slowly I'm getting used to the team and it is a very clear system and it has been good to play these minutes with my team-mates. Now I must keep working.
"The work in pre-season has been very good and I feel good physically.
"It was something that we had spoken about because as you know I have not been on the tour and stopped in Madrid to do extra work and it was best to wait to make my debut here.
Atleti enjoyed a successful campaign last term, winning the European Supercup with victory over Chelsea before lifting the Copa del Rey after beating arch-rivals Real Madrid in the final and Villa is keen to continue that winning trend.
The former Barca and Valencia man said: "Now the league begins and we are keen to challenge in all competitions.
"It's just around the corner and we have very difficult games both in the league and the Super Cup.
"We all looking to start in the best way possible."
Atletico Madrid get their Liga campaign underway against Sevilla next Sunday.