The Spaniard says he is focused only on keeping the England midfielder fit and firing and revealed that Petr Cech has an ankle injury but refused to comment on Demba Ba
Everton took the lead in the second minute through Steven Pienaar before Lampard scored a goal either side of half-time to seal the three points for Chelsea.
The 34-year-old is able to sign a pre-contract agreement with a foreign club from January but Benitez claims he is focused solely on keeping him fit and in form.
"My job is to keep Lampard fit," Benitez told Sky Sports. "He is under contract, fully committed and working hard and that is it.
"My job is to coach the players, and keep winning games and keep my opinion."
Despite the poor start at Goodison Park, Benitez was pleased to see continued progression from his team as they moved back into third place in the Premier League.
"We started the game making a couple of big mistakes and they were pushing really hard," he commented.
"But the players reacted, and that was good against very strong players who have been playing together for a long time under the same manager for ten years. That is a big advantage.
"Still we are making some mistakes but the team is getting better and the players are keen to learn, which is important."
Benitez said that the extent of the ankle injury to Petr Cech, who was substituted at half-time, is unknown, and that the goalkeeper will undergo a scan.
He refused to comment, meanwhile, on reports suggesting that representatives from the club will meet with Newcastle striker Demba Ba in order to tie up a January transfer for the Senegal international.
When asked if he could speak regarding Ba he replied: "No, because we don't talk about this business, we had a very important game today."