Gillett believes Benitez is the right man to turn things around at the club.
The Reds are on their worst run since 1987, following four straight defeats.
“We have just entered into a long-term agreement with Rafa,” he said.
“Our family is extraordinarily pleased with him, we believe he is absolutely as good as there is in the business.
“The run of results disappoints everybody. Certainly, it disappoints the fans and it disappoints Rafa.
“I have seen his television interview and I know he is disappointed. We are all disappointed, but we are in this together.”
