Garcia arrived from Lille at the start of the 2013-14 campaign and guided Roma to second behind Italian champions Juventus, who won the Scudetto by a record 17 points.
The runners-up placing capped a remarkable turnaround for the Rome-based club, having finished sixth in 2012-13.
And Garcia, who is preparing for Roma's friendly against Liverpool in Boston on Wednesday, has high expectations heading into the new season.
"We need to be ready for the start of the campaign," the 50-year-old told reporters.
"Our primary objective is of course Serie A. I am ambitious and I want to win.
"We've been working together for a week and the team is happy to be united again. That is the best foundation to work from."
With Roma set to compete in the UEFA Champions League in 2014-15, the club have been busy in the transfer market as they prepare for an increased fixture list.
Roma spent €22 million on Argentinean midfielder Juan Iturbe, who arrived from Hellas Verona.
The club have also brought in free agents Ashley Cole, Seydou Keita and Urby Emanuelson, as well as Turkish youngster Salih Ucan on loan from Fenerbahce.
Garcia said he is happy with the added depth and competition for places.
"We brought in more players because we'll play a great deal from now to December, so need a competitive squad for every game," he said.
"We're almost at the finish line for this transfer session but you never can tell right to the end.
"The only pressure on us will be from ourselves. We want to do better and that's the only way to win.
"We play with enthusiasm and it will be a tougher year with the Champions League but there's no external pressure. We'll approach it the way we always did."
