The Springboks were beaten 27-15 by Australia on Saturday - the first time since 2000 that the Wallabies have triumphed on South African soil.
De Villiers was widely booed by the Absa Park crowd during the post-match interviews and faces mounting criticism as he seeks to move the Boks away from their traditional conservative approach.
His efforts to get South Africa playing a more expansive game have led to just one win in five Tri-Nations matches.
And Hoskins warned the coach, who has only been in charge for nine games, to brace himself for a difficult week as he prepares the team for another clash with Australia this weekend.
Hoskins said: "It will be a challenge for Peter this week, especially with the way the crowd reacted to him.
"But it will also show his character as a person and coach. We will see if he is strong enough to handle it, because this is the most difficult rugby job in the world.
"Peter must understand that with South African rugby it is difficult to move away from the winning principle.
"Whatever he is trying to do with the team, winning still needs to be a priority. We're behind him and I ask people to have patience and to support the side.
"The buck stops with me and my administration. It is our responsibility and we need to back him."
De Villiers insists he will not change the team's style of play, even though it is not yielding victories.
He feels the transition to the new Experimental Law Variations (ELVs) means the changes he has tried to implement are necessary.
"Look, it's not that we wanted to change," De Villiers said. "The laws of the game have changed and we couldn't be fast asleep.
"We're just not changing quick enough, and we saw in the Super 14 we can't win games under the new laws if we don't have speed.
"The game is much more intense under the new laws and players need to make decisions quicker on the field.
"I believe we are on the right track and the players believe it as well. We just have to get used to it. We do a lot of things right, but we are sometimes just that part of a second too late and there is that one pass that doesn't stick or go outside.
"It is understandable. The Boks have been playing a certain way for years and we're trying to change it suddenly. We have to be patient.
"I'm not unhappy with the way we are playing, but it bothers me a lot that we are not accurate enough on the field."