Garcia's side have won just two of their last 12 matches in all competitions, leaving them 14 points behind Juventus in the Serie A title race.
Their one realistic chance of silverware this season remains the Europa League, as Garcia prepares his side for a last-16 second-leg meeting with Fiorentina on Thursday.
Roma come into the home leg with a slender advantage, having drawn 1-1 in Florence last week, but Garcia is aware their form must improve.
"I want to reassure everyone, I have fallen in love with this team, this Roma," he said.
"The day I feel I am no longer useful and cannot get the results and trophies then I will no longer be a part of it.
"But as long as the players follow me and listen to me, then we can win here which is my dream. It is hard to do, but that is my dream and I want to satisfy it.
"I will not give up at the first time of trouble and it is important that the players know this.
"There will be further moments like this in the future I am sure, but hopefully that is all for this season. After the rain, comes the sun."
Garcia also jumped to the defence of Gervinho and Juan Iturbe, who have struggled with loss of form and injury respectively.
"You must separate the league and Europe," he said. "For example, in continental competitions, Gervinho has played well and scored important goals. He is the same player he was when the was exciting fans at the Olimpico.
"He must try to find his European level in the league. Iturbe was injured and arrived trying to learn our game and tried to get into an acceptable condition to show his quality but I have total confidence in my players.
"However, things that are said in the dressing room will stay in the dressing room."
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