Yacine Brahimi struck 16 minutes in to condemn Barca to a fifth league defeat of the season and cap off a poor week for the Spanish champions.
Having crashed out of the UEFA Champions League to Atletico Madrid on Wednesday, Barca coach Martino pulled no punches in his assessment of their title chances.
"It's a game we should have won. The (team) rotations have not had anything to do with the result," he told the club's official website.
"We must not confuse sadness after losing with actually giving up (but) the league no longer depends on us."
Ahead of the Copa del Rey final against Real Madrid on Wednesday, Martino said his squad were determined not to let another trophy opportunity slip away.
"After the two defeats the squad feels that something important has got away," he added.
"But Wednesday's game is the final and we have to go out and win."
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