Benitez has been criticised for his selective use of summer signing Fernando Torres so far this season and Tuesday's 2-1 defeat by Besiktas left them bottom of their Champions League group.
But Hicks, who owns the club with fellow American George Gillett, told Sky Sports News: "We back Rafa. He's the right manager.
"Rafa's rotation has been his policy for three years.
"Rafa's ability to coach and manage in the Champions League should be unquestioned.
"We had a disappointing loss because we got outplayed by the Turks.
"I think we have our work cut out, but yes we can qualify. We have to win the next three games."