Striker Alvaro Negredo had the best chance to break the deadlock in the 65th minute at the Sanchez Pizjuan but Depor goalkeeper Manu, who made a string of fine saves, brilliantly blocked his close-range strike.
"We had loads of chances and played really well but the ball just wouldn't go in," Negredo said in a television interview, adding that the players had to forget their frustration and focus on Thursday's tricky Europa League clash at home to Paris Saint-Germain.
Italy striker Giuseppe Rossi set them on their way with a smart volley in the 23rd minute and added a third from the penalty spot in the 55th after Borja Valero's precise left-foot drive had beaten Carlos Kameni just after the half hour.
Brazil forward Nilmar added a fourth with just over 10 minutes remaining and Espanyol's miserable afternoon was completed when Francisco Chica was shown a straight red card for a wild challenge on Jefferson Montero.
Getafe thrashed promoted Levante 4-1 and Sporting Gijon saw off Michael Laudrup's Real Mallorca 2-0.
