A string of draws since the turn of the year has seen Roma fall away from leaders Juventus, and allow Lazio to close in behind them.
Pressure has started to build on Garcia, but he expressed satisfaction after Miralem Pjanic's goal saw the club record a first home league win since November.
"If anyone needed another demonstration that this team always leaves everything on the pitch and that we always fight until the last second to win games, then yes in this sense we offered a very interesting performance," said Garcia.
"What I enjoyed most was the tactical ability of the team to follow the instructions I gave them.
"Today the team have had the right approach to the game and when we start the game with the right attitude and then the result comes because of a very good performance, it's obvious that I'm very happy with what I've seen.
"We have to consider this victory a base from which to start building up for the next games as well. The most positive aspect is that with this victory we are sure to maintain the second position in the league no matter what the other teams behind us do in their respective games.
"And another positive thing is that we can now prepare the next game against Torino having a 'normal week' [with less pressure], which we haven't had for a while."
