Manolo Jimenez's team, who took the lead at the Bernabeu last weekend before losing 3-1 against leaders Real Madrid, head into this weekend cast adrift at the foot of the standings, nine points off safety and 10 behind Sunday's visitors.
But Garcia firmly believes Zaragoza can take a step in the right direction by winning for the first time in 14 games this weekend and says they will only have themselves to blame if they fail to do so.
"What goes through our heads is just to beat Rayo," he said.
"We have a crucial game on Sunday, as we have in all our games until the end of the season.
"We are convinced we can pull it off all together, with the support of our fans.
"They deserve for us to put in the efforts to give them a victory. The fans of Real Zaragoza, with all its history, deserve a team in the top division.
"We must continue to put in the same intensity and desire as in recent games, and then the results will come.
"It can snow or we can play in the Alps... We have to win."
On playing a direct rival, he added: "You never know what can happen at the end of the season and these details can be decisive."
Rayo's on-loan Liverpool midfielder Dani Pacheco, meanwhile, is hoping to regain the confidence of coach Jose Ramon Sandoval after returning from a month out with injury.
He told the club's website: "Finally I am back. I am very happy and hopefully starting from now the manager can return to having the confidence in me that he had at the start of the season.
"I am feeling fine but I need to gain a little more physically. I have worked hard and I am ready to help the team whenever the coach requires me."
Striker Piti and midfielder Javi Fuego could also be back in contention after resuming training on Friday.