Radja Nainggolan's 26th-minute strike was enough to lead Roma to a 1-0 victory over fourth-placed Fiorentina at the Stadio Artemio Franchi on Saturday.
Roma's victory, their eighth in succession, ensured a top-two finish in Serie A and qualification for Europe's prestigious club tournament.
"When I see my team work every day, knowing their quality in every area, I am truly happy for this achievement as they deserve it," Garcia told Sky Sport Italia.
"Now we know that at the very least we are second and can still dream of first.
"It was tough here, as we know Fiorentina are a great side and especially strong on home turf. A few minutes before going out on to the field we heard that Juventus had won, so it was even more important to win."
Roma have 82 points, eight points shy of defending champions Juventus with four games remaining.
The two teams are set to meet on May 9, a match that could well decide the Scudetto, and Garcia has not given up hope of overhauling Juve.
"Now there are four games to go, we are sure of a place in the Champions League," he said. "We will prepare for the game with Milan at a packed Stadio Olimpico and are still hungry for success.
"It has been an extraordinary season, but we can still make it an exceptional one. Anything that comes now is a bonus.
"We will enjoy this victory tonight, we have 82 points and both the team and coach want more. That's all that counts tonight."
Roma midfielder Adem Ljajic, who was up against his former club, remains slightly hopeful of winning the league.
"It went well, we won and got the victory," said the Serbia international.
"Before the match our objective was to qualify for the Champions League and we achieved it. Now we have to look forward and will not give up.
"There isn't much of a chance for the Scudetto, but we won’t give up anyway. Juventus still have to play at the Olimpico, after all."
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