Sunderland were beaten 1-0 by Jurgen Klopp’s side at the Stadium of Light, but Allardyce saw reason to be positive after the fixture.
The 61-year-old boss felt that Brown’s experience had been invaluable to his team, and he moved to publicly praise the former Manchester United defender after the contest.
“Wes came in and did a fantastic job for us; he used his experience with John and Younes out,” Allardyce said.
Allardyce also had kinds words for the Sunderland supporters, who he felt got behind the team throughout the match.
"The fans were superb tonight," he added. "They were disappointed, like us, but they were terrific and tried to spur the lads on.
“Every time we were in the final third they were willing us to get a goal, but sadly we couldn’t produce the right amount of quality to get one.”
Liverpool’s win over Sunderland was secured when Christian Benteke netted soon after half time with a well-taken finish.
The Black Cats’ performance was still an improved one, though, and they will be hoping to build on their display over the coming weeks.
Sunderland are in dire need to start collecting points, as they are in serious danger of being cut adrift.
The Wearsiders are already seven points away from safety, and they have lost their last five Premier League matches.
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