The hosts broke the deadlock after 36 minutes Aron Donam He intercepted the ball in midfield, broke into the box and scored with a deflected shot before Thijs Dalinga doubled the advantage in the 58th minute.
A Christian Caceres own goal in the 73rd minute put Liverpool one back, but Frank Magri The hosts restored their two-goal advantage three minutes later, slotting in a deflected cross from close range.
Diogo Jota The Premier League side gave hope when he dribbled into the box and slotted the ball into the bottom corner.
Luis Diaz, whose father was released by the kidnappers on Thursday, started the match for Liverpool but made little impact and was replaced by Jota after nine minutes.
Liverpool top Group E, two points ahead of Toulouse.