Midfielder Alonso came off the bench with six minutes remaining as Espanyol officially opened their new stadium, and reports in Spain indicate it may be his final appearance for Liverpool.
Luis Garcia - a namesake of the former Liverpool player - put Mauricio Pochettino's side ahead after 19 minutes and former Chelsea reserve Ben Sahar scored a second-half double to give Espanyol an impressive win.
The Barcelona-based team struggled to put teams under pressure at their previous ground, Montjuic, where the stands were far away from the pitch.
But the home side were able to feel the warmth of a sell-out crowd at their new home in Cornella-El Prat, and looked to boss the game early on.
Liverpool began well and Steven Gerrard tried his luck from long range early on, only to see his effort sail wide.
The Reds captain then almost gave the visitors the lead after 18 minutes, when he crashed a fierce effort against the bar.
A minute later, Liverpool were behind as former Celtic midfielder Shunsuke Nakamura played in Luis Garcia and the Spain forward beat international team-mate Jose Reina with a neat low finish.
Gerrard curled a free-kick against the post from 20 yards eight minutes later as Rafael Benitez's side sought a quick response.
Espanyol were proving hard to break down and the Catalans thought they had gone two goals up three minutes before half-time, when Raul Tamudo fired clinically past Reina.
However, the veteran striker was ruled offside and the home fans had to be content with a one-goal lead at the break.
Philipp Degen, Andrea Dossena, Ryan Babel and Jay Spearing came on for the visitors at the break, replacing Glen Johnson, Emiliano Insua, Yossi Benayoun and Javier Mascherano.
Espanyol made five changes themselves, but displayed more urgency and went 2-0 up after 62 minutes.
Jose Callejon's pass found Sahar in the area, and the Israel striker slid the ball under Reina.
Benitez brought on Albert Riera, Andriy Voronin, David N'Gog and Damien Plessis late on, and Alonso made his brief appearance six minutes from the end.
But Espanyol wrapped up a fine win minutes before the end, when Sahar netted after Reina could only parry Ferran Corominas' close-range effort.