The Giallorossi travel to Cagliari on Sunday looking to keep up the pressure on league leaders Juventus.
Roma beat Parma 4-2 in Wednesday's rescheduled game to move to within eight points of Juve.
The outcome was Roma's fifth straight win and has left the Giallorossi in second place, nine points clear of Napoli, who are third.
"We wanted to reduce the gap with Juve and we did just that," Garcia said to Gazzetta dello Sport. "Until it becomes mathematically impossible we have to keep going and try to catch Juventus.
"I don't think our second position is safe just as I don't think that Juventus' top spot is.
"We must believe it is possible and not give up. We have to continue to win."
Juve bounced back from their 2-0 defeat at Napoli, only their second loss of the campaign, with a 1-0 triumph at Lyon in Thursday's Europa League quarter-final first leg.
The Bianconeri host Livorno on Monday before squaring off against Lyon at the Juventus Stadium three days later in the return leg.
Parma have lost just twice at the Ennio Tardini Stadium this season and host third-place Napoli on Sunday.
Fiorentina know that a defeat against Udinese in Florence could see them drop out of the top four.
The Viola are fourth, three points clear of Inter Milan, who host relegation-threatened Bologna on Saturday.
AC Milan travel to the Luigi Ferraris Stadium to face Genoa on Monday looking to make it three league wins in a row, something they have failed to achieve this season.
Lazio go into Sunday's home game against Sampdoria looking to remain in the race for Europa League football.
The Biancoceleste trail four points adrift of Inter, who hold the last European qualifying spot.
Atalanta are the hottest team in Serie A with a club record six consecutive victories heading into Sunday's game against Sassuolo.
Their impressive run has seen the Bergamaschi climb to seventh place.
Hellas Verona halted a four-match losing streak with a 3-0 triumph over Genoa last time out.
The promoted outfit go into Saturday's derby at Chievo in ninth place, 16 points clear of their city rivals.
Bottom-side Catania have lost their past four league games and trail six points behind safety.
The Sicilian outfit have mustered just two wins this year and host Torino on Sunday.