Garcia cited the lack of new signings as a reason for the current negative feeling at his club, after a number of key players - including Miguel Torres, Abdel Barrada and Xavi Torres - were allowed to leave in the summer
The only new face at Getafe this season is former Celta Vigo left-back Roberto Lago, although Sergio Escudero and Alexis Ruano, who spent last season on loan at the club, have been made permanent signings.
Getafe host newly-promoted Almeria in their second game of the season and Garcia is hoping for a change of fortunes.
He told reporters: "This has only just begun. I think there is too much pessimism among the fans, but we have to demonstrate that we are a team with ambition, hope and good spirits.
"We will go all out to win the game [against Almeria] and be competitive at home, as we have been in the last two seasons. We have to pick up points at home, that's vital.
"It's true that there aren't many new faces around, but Escudero and Alexis are new signings, even though they were here last season and so we aren't treating them as new signings.
"Important players have left, but we have a competitive squad. We'll make a general evaluation when the transfer window shuts.
"Right now everyone needs to support us."
Almeria also ended their first game of the campaign without any points, conceding two late goals to lose 3-2 at home to Villarreal despite taking the lead twice in the match.
Rojiblanco coach Francisco Javier Rodriguez has a full squad to choose from for the trip to Madrid.