It was the world champions' third consecutive defeat in the Tri-Nations and saw them slip behind the Wallabies into third in the official IRB rankings - their lowest position since winning the World Cup last year.
"I would like to make it clear that Springbok coach Peter de Villiers, his management team and playing squad have my unequivocal backing and that of the South African Rugby Union president's council and of the board of SA Rugby (Pty) Ltd," Hoskins said in a statement posted on the SARU's official website on Monday afternoon.
"Although we share and understand the frustration and disappointment of supporters, speculation about the coach's future is pointless.
"The two most disappointed people in South Africa today are, in fact, Peter de Villiers and captain Victor Matfield and we know they will be doing everything in their power to achieve victory at Coca-Cola Park in Johannesburg on Saturday."
De Villiers was a controversial selection to lead the Springboks following former coach Jake White's departure at the end of last year.
Heyneke Meyer was the favourite to take over the role after leading the Bulls to the Super 14 title, however the SARU opted to go with De Villiers who became the nation's first black coach.
The 51-year-old's tenure began well with home victories against Wales and Italy, however his side have struggled in the Tri-Nations winning just once in five games.
Saturday's defeat ended their hopes of winning the annual tournament and some reports have suggested De Villiers may be shown the door when the SARU conduct their end-of-tournament review.
Hoskins has however moved to play down such talk, adding: "Let me put an end to speculation that the post-Vodacom Tri-Nations review will in some way be pivotal to the future of the coach.
"That is not the case. It is an entirely normal quarterly review such as every Springbok coach has undergone.
"I would like to underline that Peter's future is secure - we are not in the business of sacking Springbok coaches within three months of them playing their first match."
The Springboks face a return encounter against the Wallabies in Johannesburg on Saturday, but De Villiers' hopes of achieving a much-needed win have not been helped with a number of his first-choice players under injury clouds.
Winger JP Pietersen was on Monday ruled out of the match after he suffered a hamstring tear in last weekend's defeat while Matfield (groin) and hooker Bismarck du Plessis (knee) are doubtful starters.
Star winger Bryan Habana's hamstring injury will also be assessed later in the week after he was forced to sit out the loss against the Wallabies.
Sharks winger Odwa Ndungane has been called to the team's base in Sandton to replace the injured Pietersen.