The loss at Estadio Nuevo Los Carmenes compounded a miserable week for Barca, who were knocked out of the UEFA Champions League at the quarter-final stage by Atletico Madrid in midweek.
Gerardo Martino's side were missing several first-team players, with Gerard Pique, Marc Bartra, Victor Valdes and Carles Puyol all out, while Dani Alves, Xavi, Alexis Sanchez and Jordi Alba were all left on the bench.
Although the visitors dominated proceedings, Yacine Brahimi's 16th-minute strike was enough to earn Granada a huge boost to their survival chances, while providing a serious blow to Barca's title hopes - and Montoya acknowledged that he and his team-mates were hurting.
"Mentally we're pretty screwed up," he told the club's official website. "We could have won but we couldn't capitalise on our chances. We gave it our all but in the end it wasn't possible.
"We will fight for the league until the end, we still have games left and hopefully our rivals lose points.
"I ask the fans to support us on Wednesday (against Real Madrid in the Copa del Rey final. We want to dedicate a victory to them."
Midfielder Andres Iniesta echoed Montoya's disappointment and went on to suggest that they are currently taking backward steps.
"Sometimes it's hard to find an explanation, we did everything we could to score," he said.
"It's a step backward. We made a mistake in the play that led to their goal and that really hurt us.
"It hurts to take this backward step at this point in the league, when there's so little left for the year to be over."
