The Giallorossi beat Parma 4-2 in Wednesday's rescheduled league match to move within eight points of Juve with seven games remaining.
"We wanted three points against Parma and we got them," Garcia said to Gazzetta dello Sport. "We had nothing to lose against Parma and all to gain.
"We have to compliment Parma because they came to Rome determined to win and played at a high level."
Their midweek outcome was Roma's fifth straight league win and left the Giallorossi in second place, nine points clear of third-place Napoli.
"I don't think our second position is safe just as I don't think that Juventus' top spot is," Garcia said.
"Until it becomes mathematically impossible for us, we have to keep going and try to catch Juve.
"We must believe it is possible and not give up.
"We have to continue to win."
Roma have the strongest backline in the competition with just 17 goals conceded and the second best attack behind Juventus with 39 scored.
"We are playing well," Garcia said. "The fact that we have the second best striking force in the competition means that everything is working well.
"The important thing is that we play together and that we attack our opponents for 90 minutes.
"I expect my team never to give up, not only in the competition but in every game."
The Giallorossi travel to Sardinia to face Cagliari on Sunday while Juve host Livorno 24 hours later.