The Serie A leaders go into Thursday's game against bottom-side Chievo at the Stadio Olimpico looking to set a new record of 10 successive victories at the start of the season.
Michael Bradley's solitary goal handed Roma a 1-0 triumph at Udinese on Sunday to see the Giallorossi go five points clear of both Napoli and reigning champions Juventus.
However, Garcia does not want any relaxation from his players.
"It is great to have won nine straight games but what I would like is for people to remember us at the end of the season, perhaps with a trophy in our hands," Garcia said to Roma Channel.
"We have to focus on Thursday's game.
"Everyone, even at (Roma's training ground) Trigoria think that the game against Chievo has already been won.
"However, this game is going to be the most complicated one since the start of the season."
Garcia's troops have been outstanding and they boast the best defence and attack in the division, with 23 goals scored and just one conceded.
The Romans are still without captain Francesco Totti but are hoping to recover forward Gervinho, who missed the game at Udinese with a muscular problem, while defender Maicon must serve a one-match ban.
Rivals Chievo have yet to see the light at the end of the tunnel.
The men from Verona, who had a private audience with Pope Francis at the Vatican on Wednesday, have struggled in every department.
Sunday's 2-1 loss to Fiorentina was Chievo's seventh defeat of the campaign and dropped the Flying Donkeys to the foot of the standings with four points taken.
With just one victory taken this campaign, a defeat in the Eternal City could prove costly for Chievo coach Giuseppe Sannino.
"I believe I am doing the best I can for the team," he said.
"I feel very much the coach of Chievo. However, we have not achieved the results we expected and we need to turn things around as soon as possible."
Chievo have found the net just seven times while they have conceded 17 goals so far.