The in-form striker was substituted at half-time after a clash of heads with David Unsworth.
He underwent scans on Saturday night and faces a battle to be fit for the Worthington Cup semi-final, second leg at the Lane on Wednesday.
Manager Glenn Hoddle revealed: "Les has got concussion and it is a problem for us with Wednesday's game coming up.
"He will go for some scans and we'll see how he feels. But if we do lose him, then it will be a blow because he is on fire in front of goal."
Les scored his eighth goal in nine games and 14th of the season to put us ahead in the fourth minute against Everton.
But the Merseysiders hit back with David Weir's fantastic volley just three minutes later and defended doggedly as we pushed for a winner.
"Les can't remember too much about what happened," added Glenn. "He came over to the bench and said he wanted to carry on, so we told him he was Pele!
"But at half-time he was feeling groggy so we took him off because we have one eye on what is happening long-term."
Les Ferdinand is doubtful for this week's crucial clash against Chelsea after suffering concussion in the draw with Everton.