Palmer, 23, was the third Chelsea player to be removed from the game within 21 minutes, setting a Premier League record for the earliest three substitutions by a team.
Two other players, Estevao and Pedro Neto, were also taken off due to an early red card by Robert Sanchez.
Palmer appeared to be experiencing discomfort in his groin during the game, which may be a recurring issue from an earlier injury this season.
He left the field immediately to undergo further evaluation.
Maresca discussed Palmer's condition with the press after the game, stating that the midfielder had undergone tests to assess his fitness level.
"Cole underwent a test this morning to determine if he could play in the game," Maresca said. "Unfortunately, he was not 100% fit, which is why he was substituted."
