Alcaraz replaced Juan Antonio Anquela in January but Granada are still struggling in 16th place, having taken just one point since their last victory over Deportivo on February 9.
Alcaraz, who had a spell as Granada coach between 1995-98, is targeting a much-needed win against Levante as a defeat could leave his side relying only on goal difference to keep them out of the relegation zone.
"It's a home game so we have the target of winning," he said.
"Levante are a competitive team and give the opposing team a few issues.
"We must be faithful to our tactics - The important match is the most imminent. We must always try to get a win to boost the mood and give much confidence to our staff."
Despite the poor run of form, Alcaraz is still confident his players are up for the fight.
"I see the team working with enthusiasm and attitude," he added. "We could have won virtually all of our matches."
Granada's chance of picking up a result against mid-table Levante was given a boost on Thursday evening.
Juan Ignacio Martinez's side, who are on a six-game winless streak in the league, took Rubin Kazan to extra time in their Europa League clash in Russia before bowing out of the competition.
Levante remain in the top half but their recent run of form must change if they wish to challenge for the European places again.
Martinez will have a job on his hands lifting his players' spirits after admitting heads dropped in the wake of their defeat in Russia.
"I'm very proud of my players," he said. "We are crestfallen but at the same time we must be very proud of the team's history. We have done brilliantly in the Europa League."