The Madrid outfit are currently ninth and six points behind sixth-placed Valencia and the final European spot, although the team that finishes seventh could also be granted a berth in the Europa League if Malaga's UEFA-imposed ban from European competition next season is upheld.
Getafe host Espanyol on Sunday, a game that will be crucial to how they finish the season.
"Now is the time for everyone to be positive and make the final push. That includes the press, the fans, us and everyone involved in the club," said Garcia in a press conference.
"The team has defects, of course, as do Barcelona, Real Madrid and Atletico Madrid. But we also have many virtues. We had a bad game against Valladolid [where they lost 1-2 last weekend] but before that we went seven games without losing.
"We are among the top 10 sides in the league and we have to produce an amazing show of unity like never before."
He added: "On Sunday we have to go out and impose ourselves on Espanyol on the pitch. Everyone must dig in. We have to do everything that is in our hands so that Getafe can play in Europe next year.
"We are close, and that can only be because of the good work we have done this year. We have to transmit enthusiasm and stamp out negativity. We've got a lot to play for against a team that are very, very difficult to beat."
Garcia revealed left-back Mane could return to the starting line-up for the first time in three months since injuring his knee.
Mane would deputise for Alexis, who is suspended for the game after being sent off against Real Valladolid last weekend, and will serve the first game of a four-match ban.
Miguel Torres, Sergio Escudero and Adrian Colunga are all injured, but Pedro Leon is expected to be fit enough to at least be named on the bench.
Espanyol full-back Joan Capdevila believes that teams are much more afraid of the Catalan club than they were earlier in the season.
"We have won the respect of our opponents, now they look at us differently," he told reporters.
"We are a solid team and teams can't play against us with the same fluidity as before, especially when they come to our place."
The former Spain international is eyeing up the trip to Getafe as a chance for his side, currently on 40 points, to confirm their status in the top flight next season.
"This is a game that will mark the future of our season. If we win we will have achieved our first goal for the season, which is survival," he said.
Forward Sergio Garcia has recovered from injury in time for the match, but Raul Rodriguez is suspended and right-back Felipe Mattioni is injured. Sergio Tejera, Cristian Gomez and Christian Alfonso have all been recalled to the squad.