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."
‘Sir Alex told Van Persie to watch my goal back at Anfield for some shooting tips! It was a beautiful goal, though. It’s a shame that I didn’t do it more often’: Manchester United cult hero recalls stunning strike against Liverpool
‘So many times when we played Manchester United, arguments would start before the first whistle had even blown – the players would try to kill each other with their eyes’ Former Arsenal star remembers famous Premier League rivalry
