"You will never win the fans over if the majority don't want you," Graham told the Sunday Mirror. "All Benitez can do is work hard with the players, put over his ideas and win silverware.
"He is a professional and I am sure he will not be affected by what is being said.
"The fans forget that watching the club is their hobby. To the managers, it is their job, their livelihood. They have to get the results to pay the bills.
"No matter what Benitez does, he won't win over the fans who do not want him. And he will know that."
Graham added: "He will just try to win games to get the fans thinking about results rather than thinking about him. That is all he can do."