Roma, second in Serie A, have faded badly since the Christmas break, winning only one of their last 10 games and dropping 14 points behind leaders Juventus who look almost certain to wrap up their fourth successive title.
Garcia's future at the club is now uncertain with speculation that former Napoli and Inter Milan coach Walter Mazzarri could replace the Frenchman next season.
"The day I realise I can no longer help the club to win trophies, I will make way for someone else," Garcia told reporters.
"But as long as the players are with me, I want to win things here because that's why I came. With this team, in this environment which is perhaps the toughest in the world, it's still possible to win things.
"I said that I would never be a burden because I've learned to love Roma.”
Garcia also recognised that Ivorian winger Gervinho had not been at his best.
"Gervinho is the same player that brought the Olimpico crowd to their feet with some of his play. He needs to get back to his best," he said.
But Garcia, whose side host Fiorentina in a Europa League round of 16 second leg tie on Thursday after drawing 1-1 in the first game, said some of the criticism was over the top.
"I wasn't shouting from the rooftops over the first six months of the season when things were going well," said Garcia. “Nor will I now get down in the dumps and think we're doomed now.
"You'd think we were fighting relegation given the mood about the place, and yet we're still on course to go through to the next round in Europe."
(Writing by Brian Homewood in Zurich; editing by Justin Palmer)
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