Barbara Bonansea scored the only goal midway through the first half, eluding two defenders before shooting from close range.
For the hosts, Asisat Oshoala had a goal ruled out for a foul.
The match marked Liverpool manager Matt Beard's final game in charge before moving to Boston Breakers in the USA.
Liverpool dominated long periods without turning pressure into goals.
Ashley Hodson forced two good stops from goalkeeper Camelia Cesar, while Lucy Staniforth saw her two direct free-kicks well saved.
Other than the goal, the Italian side created few clear openings. Chiara Marchitelli and Valentina Cernoia had shots from outside the area, but both were straight at keeper Libby Stout.
Beard said: "I was pleased, we've done everything but score again, we threw the kitchen sink at them in the second half.
"To be fair to Brescia, they defended really well which restricted us.
"And over the course of the two ties, they probably deserve to go through."
Liverpool Ladies: Stout, Harris, Murray, Omarsdottir, Ryland, Staniforth (Williams 70), Zelem, Oshoala, Hodson, White (Dale 79), Dowie (c).
Unused subs: Darbyshire, Beckwith, Schroder, Pacheco, Smorsgard.
Brescia: Marchitelli (Cesar 32), Gama, D'Adda (Boattin 61), Linari, Cernoia (c), Eusebio, Rosucci, Bonansea, Girelli, Sabatino (Alborghetti 76), Tarenzi.
Unused subs: Serturini, Ghisi, Lenzini.
Referee: S Frappin
Attendance: 387
Liverpool Ladies have been knocked out of the Champions League after losing 1-0 at home in their last-32 tie, suffering a 2-0 aggregate defeat.