Interim Blues manager Benitez will take a team to Goodison Park this weekend for the first time in more than three years but the passage of time is unlikely to spare him the role of pantomime villain.
Everton fans devised plenty of unpleasant chants about Benitez during his six years in charge of Liverpool and he said: "I don't think they will be supporting me the whole time but the main thing for me is that my players do their job."
The Spaniard, who still lives on the Wirral near Liverpool, added: "I have a good relationship with people in the city and what I expect is to find a manager up there with a team who want to win."
Quizzed about his small-club jibe ahead of Sunday's game, Benitez joked: "You have a good memory."
He added of Everton: "I think they are doing a good job. They are doing well, they have less resources than other teams and are still competing. They are near the top of the table so credit to them."
They have lost only two league games - the joint best record in the top flight - and are one of only two clubs unbeaten at home.
Benitez, who has won on his last three league visits to Goodison Park, said: "It is a good team and a tough game for sure. We have to be ready. For us, we have to be ready physically as well as mentally for the game.
"They have been doing well in the past year and we know that Goodison is a difficult place to go to."