Garcia claimed Roma "responded magnificently" after copping a second-half red card and going behind thanks to Carlos Tevez's 64th-minute free-kick.
Seydou Keita would eventually score an equaliser for the home side with a header 12 minutes from time, although the 1-1 draw left Roma nine points adrift of the title-holders with 13 matches remaining.
But Garcia refused to get down about the result - despite many pundits claiming it secured a fourth straight Serie A title for Juventus.
"We responded magnificently," he said, according to Roma's official Twitter account.
"Despite being a man and a goal down, we fought back to draw: we're alive and kicking."
Garcia underlined the importance of his substitutes at the Stadio Olimpico, claiming Alessandro Florenzi, Juan Iturbe and Radja Nainggolan changed the match.
After a lacklustre first half, which saw Juventus defend with a back five, Garcia sacrificied Adem Ljajic, captain Francesco Totti and veteran Daniele de Rossi.
Iturbe won the free-kick that led to Keita's goal, while Florenzi provided the cross for the Malian midfielder.
"The substitutions worked for us tonight." Garcia said.
"They helped the team step up a gear."
The French coach added: "We hurried things in the first half. We needed to move the ball around more and make the most of the wide areas."
Having missed the chance to take a chunk out of Juventus' lead, Roma look set to miss out on the Scudetto but Garcia insisted the capital club will not give up yet.
"There are 13 games left to play. If we want to keep up the pressure on Juve, we have to hold onto second place," he said.
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