Inconsistent performances in the second half of the season have seen Roma fall nine points behind Serie A leaders Juventus and go out of the Coppa Italia to Fiorentina.
They continue to make progress in the UEFA Europa League – where they meet Fiorentina in the last 16 – but reports had linked Garcia with a move away.
However, Roma's American owner has rubbished those rumours and given the Frenchman his full backing.
He said: "Of course he will be our coach, why would he not be?
"Have you heard it from me? He's not going anywhere, it's my call, it's ridiculous.
"He's had to deal with so many injuries, and change formations so many times."
Pallotta also praised the effort shown by Roma's players as they came back from a goal down against Juve on Monday to earn a 1-1 draw at the Stadio Olimpico.
"At first it wasn't going well, but then when we started to play in the last half an hour I thought we could win," he added.
"There are a lot of teams in the world who, if they were a man down against Juventus, would surrender. Most teams would give up and go home, but we battered them in the last minute."
