Goals from midfielders Joe Allen and Jordan Henderson made it five wins from five for Brendan Rodgers' side during preseason as a full house saw the home side dominate the almost entire 90 minutes.
Gerrard apart, the loudest cheer of the day was reserved for wantaway striker Luis Suarez, whose future continues to be unresolved despite his wishes to leave the club.
Rodgers again left Suarez on the substitutes bench, with the striker suspended for the opening weeks of the Premier League season, and gave Iago Aspas another chance to stake a claim for a starting berth against Stoke on the opening day of the season.
The summer signing from Celta Vigo has shown good form during preseason, and he should have given the hosts the lead inside five minutes after Allen latched onto a loose pass from Andreas Samaris before playing the striker in. His shot, though, was straight at Balazs Megveri.
Allen and Aspas were at the heart of much of Liverpool's attacking play, and the pair combined again midway through the first half when the striker's intelligent flick was volleyed over by the former Swansea man.
He made amends seconds later, though, as a mix-up in the Olympiakos defense allowed Lucas to find Aspas on the left, and the forward's center was perfectly timed for Allen to turn in at the back post.
More chances came and went the Anfield outfit as Aspas was again denied by Megveri before Allen headed a Gerrard cross wide while the Greek champions failed to test Simon Mignolet during the opening 45 minutes of his home debut.
The pattern of Liverpool dominance continued after the break as Phillippe Coutinho fired straight at Megveri while Raheem Sterling went close with a lobbed effort that fell just wide of the post.
