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

In a major report drawing together findings on Scottish schools over a four-year period, he highlighted "variable" standards in primary education.
Dr Maxwell said financial constraints had been a challenge for education.
But he said that, overall, inspectors had been impressed with the commitment shown by leaders and staff.
Dr Maxwell said he had found "many strengths" across all sectors of education and examples of "outstanding innovative practice".
The report - Quality and Improvement in Scottish Education 2012-2016 - set out five key areas for improvement:
Education inspectors said Scottish education had gone through a period of "very significant reform".
Speaking at Larbert High School, where the report was launched, Dr Maxwell said: "Overall, our inspectors have been impressed by the strong commitment of leaders and staff to improving outcomes for children and young people.
"High-quality leadership will be essential to ensuring that sufficient progress is made, across all sectors, in order to continue to secure improvements in education practice and achieve our national ambition of ensuring all learners can reach their potential, regardless of their background.
"We believe that addressing these five priority areas for improvement effectively will make a decisive contribution to achieving the twin aims of excellence and equity for Scottish learners which is at the heart of the National Improvement Framework."
EIS General Secretary Larry Flanagan said the report was a "substantial piece of work" which highlighted Â£the continuing strengths of Scotland's education system including the very high levels of commitment that are demonstrated by Scotland's teachers".
He added: "Education Scotland itself has to be more proactive in supporting schools and teachers.
"Criticism has been voiced by many members, for example, about poor support and a lack of communication around the introduction of new national qualifications.
"As a well-funded agency it needs to deliver that crucial support as well as provide a critical voice to government policy making, which should be evidenced based at all times."
"One thing that is very clear throughout the report is the degree of change compared to the scale of cuts throughout education, and this will continue to create challenges until the politics of austerity cease and education budgets are substantially increased."
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.
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Scotland's Chief Education Inspector Bill Maxwell has said key aspects of education need to be improved.