The on-loan Chelsea striker reportedly left Anfield with his ankle in a cast after colliding with team-mate Gareth Barry as Steven Gerrard headed the opening goal in a 4-0 victory for Liverpool.
Everton lost left-back Bryan Oviedo to a double fracture of his left leg in the FA Cup win at Stevenage on Saturday and boss Roberto Martinez fears Lukaku also looks set for a lengthy spell on the sidelines.
"It does not look good for Romelu Lukaku, he picked up a bad injury. It was that type of night when everything went against us," Martinez said.
Daniel Sturridge scored two goals in as many first-half minutes after Gerrard had opened the scoring.
Luis Suarez added a fourth goal early in the second half and Sturridge wasted a chance to complete his hat-trick when he blazed a penalty over and into the Kop after Tim Howard had upended Raheem Sterling.
Martinez talked up Everton's chances of securing their first win at Anfield since 1999 in the build-up to the game, but he was left puzzled by his side's display as they were put to the sword by their city rivals.
"For different reasons we could not maintain the normal intensity, we became exposed and were naive. We gave the ball away far too easily," he added.
"We wanted to perform so well for the fans and we have been terrific all season. We need to bounce back straight away and perform in the manner we did before."
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