Allardyce also suggested that certain members of Palace's squad would have been "on the pop" following their Wembley success, but Pardew - having seen his side fall to a 1-0 defeat at St James' Park - has defended his players.
"They're prehistoric comments," he is quoted as saying by Chronicle Live. "Three or four of my players don't drink. Perhaps he meant Coca-Cola."
Palace assistant Keith Millen also responded to the comments, adding: "We made it a really tough game for Newcastle, who are fighting for their lives. Sam can say what he likes about us, but we know we are very professional in what we do."
Allardyce's Sunderland side rescued a 1-1 draw in their meeting with Stoke City elsewhere on Saturday afternoon to keep their own survival hopes alive.