The tourists trail the current series 2-0 Down Under following a 218-run defeat to Australia at the Adelaide Oval on Monday, as England fell for 172 runs during their first stint at the crease.
"The first innings collapse in Adelaide was as embarrassing a performance as I have been involved in with England," Prior, who was out for a duck in that first innings," he told The Telegraph.
"The disappointing thing was how people got out. You are representing your country and that is not a performance anybody expects from this team."
Australia can reclaim The Ashes and end a run of three straight series losses to England with another win in the third Test, which gets underway at The WACA in Perth on December 13.