A crucial period lies ahead the Eagles in their final 10 games of the season, starting with the visit of Leicester City to Selhurst Park on Saturday afternoon.
Speaking to Palace TV, Hodgson said of the supporters: “They are absolutely vital.
“If you listen to people from the outside, when they discuss the chances of Crystal Palace surviving, one of the first things they talk about is the fanbase, which has been incredible throughout the years here.
“During my [last] four years here, it was absolutely wonderful. There were many times they pulled us through games and gave us that energy when we were flagging. They boosted our spirits, and of course they have always been very supportive of the team.
“From our point of view, we are totally and utterly dependent upon them if we are going to pull this off.