Atletico travel to Estadio Ramon Sanchez Pizjuan on Sunday to face a side without striker Alvaro Negredo and winger Jesus Navas, who have both joined Barclays Premier League side Manchester City this summer.
The capital side have in turn lost star man Radamel Falcao to Monaco, so Garcia is not taking anything for granted and is relishing what is set to be a tough opening fixture.
"We really want to start competing," Garcia said on the Atletico website.
"The league opener is in Seville where we always like to play because it's a challenging ground. We really want to start winning.
"Sevilla have always been able to sell important players and replace them later with competitive people. It will be a tough game. The people who are new are bringing many things."
Atletico finished third last season, nine points behind capital rivals Real Madrid and a huge 24 points behind champions Barcelona.
This time around, Garcia is focused on making a strong start.
"The team wants to keep improving," he said. "The goal always has to be to match all the good things that we have done and in that sense improve our records."
Sevilla coach Unai Emery knows to expect a tough examination in his side's first league fixture.
"Atletico have the advantage of being the third best team by merit," Emery told Sevilla's official website.
"But we have the hope and the belief that we can compete with them and beat them over the course of the season.
"If we win on Sunday then we are ahead of Atletico and that is the goal. We are ambitious."