Both Juve and Roma have maximum points through three fixtures, with Garcia's men earning a 2-0 win over Cagliari at the Stadio Olimpico.
Garcia was quick to underwrite his side, who are yet to concede a goal in 270 minutes of league action this term.
"We cannot say that it is a title race between Roma and Juventus after just three games," Garcia said.
"I think there are strong teams that can fight for the top of the league every season. I think there are several teams who could still challenge for the trophy but we'll see.
"Roma is the most important thing to me. We want to get the three points every time we get on the pitch."
Garcia said their brilliant opening, which saw them strike via Mattia Destro and Alessandro Florenzi inside 13 minutes, showed their hunger in the domestic competition.
"I really liked the start of the game," Garcia said.
"It was very important to start well and show that we have the same motivation and willingness to win in the league as in the Champions League."
Garcia said his side's ability to get the job done in sweltering heat - the temperature peaked at 29 degrees Celsius in the capital - was a further sign of their ability to overcome hurdles.
"This victory is a good sign of how we are maturing as a team," he said.
"As we play more games in both Serie A and the Champions League we have to learn how to manage games like this one.
"We scored twice with Mattia Destro and Alessandro Florenzi; a two-goal win is not bad considering the hot weather conditions in Rome we experienced today.
"At the end of the day we are at the top of the table with nine points, not having conceded any goals so far this season.
"All these figures suggest that we made a good start to the campaign so far."
