Leo Baptistao's early strike and Ruben Vezo's own goal saw Granada fall 2-0 behind inside the first 10 minutes.
On-loan Manchester United midfielder Andreas Pereira replied for the home side before the break, but Adams's seven-game spell in charge ended pointless.
Former Arsenal and England skipper Adams was appointed head coach until the end of the season on April 10 after the sacking of Lucas Alcaraz, but relegated Granada finished bottom of the table.
Espanyol raced into an early two-goal lead as Leo Baptistao converted from close range in the third minute and five minutes later his pass into the six-yard box was inadvertently turned home by Granada defender Vezo.
Granada goalkeeper Uche prevented Espanyol extending their lead midway through the first half when he saved well from Leo Baptistao's header.
Adams's side reduced the deficit in the 22nd minute through Pereira, who crashed home a shot into the bottom corner from outside the penalty area after being set up by Adrian Ramos.
Pereira fired inches wide early in the second half and David Lomban was just off target in the 63rd minute as Granada chased an equaliser.
Granada continued to force the issue, but could not find a way back and although they went down fighting, Adams's side took only one point from their last 13 league matches.