There is no love lost between Benitez and West Ham boss Allardyce.
He said: "We don't have sympathy for each other.
"We compete against each other, toil, play mind games and tactically have to outweigh each other. And we've come out on top today."
Allardyce suggested Benitez was in a Catch 22 situation.
"You can't do it if the fans aren't behind you," he said.
"But the only way you can get the fans behind you is to win. If you're winning, the fans will always, always be behind you."