They never implicated Carol Marcus during the film. She had the full trust of Spock, because she was the Admiral's daughter.
Kirk knew before anyone else that it was sabotage. When they are about to regain warp power and Chekov says "I take full responsibility for the failure". Kirk says "I don't think it was your fault." Or something like that.
The film states specifically that it was the Admiral. We could assume that he had someone do it for him, but his name is used to identify who did it. This is mentioned twice during the film. Once by Spock when he's talking to Kirk, and once by the Admiral when he's talking ship-to-ship with Kirk.
The Admiral's plan went wrong. The Enterprise was support to fire the torpedoes first before the ship broke down stranding them in Klingon space. Because it broke down first, Kirk takes a landing party to capture Khan. Kirk never intended to fire the torpedoes anyway.
They try to report back to Earth that they captured Khan alive, but they never get a response. Uhura says someone is blocking the signal, then the Admiral appears in his new ship to destroy the Enterprise.
The Admiral assumed the torpedoes would start a war, the stranded Enterprise would be destroyed by Klingon's covering up what the Admiral did.