Ayoze Perez hit the winner on 73 minutes.
Benitez wished the media a happy new year and then praised his players' efforts after a second game in two days.
"Today was another example of a team working hard against a team working hard too who made it very difficult for us.
"The fans were really good. We have seen the fans away last year and this year really fantastic. It's a perfect day for them and like so many times last year they go home with smiles on their faces."