Caesar's power ended with his death. In the political vacuum that existed after the assassination, Antony grabbed power for himself by exercising his shrewd understanding of human nature. It was his ability to understand and manipulate others that accounted for his being allowed to speak at Caesar's funeral, turn the crowd, and plunge Rome into civil war. It wasn't Caesar-in-death who influenced the crowd. After all, moments before Antony's speech, Caesar had still been dead and the crowd had embraced Brutus.
It might be argued that Caesar exercised power after death because Antony sought to avenge his murder, but if so, it was short-lived. Antony's private speech over Caesar's body, mourning him and vowing revenge, seemed heartfelt, but as soon as Antony seized power and made his alliance with Octavius and Lepidus, his mourning and high-minded motives came to a screeching halt as he consolidated power and the spoils of war for himself. He purges the Roman Senate of those he perceives as enemies, he alters Caesar's will, and he cuts Lepidus out of the financial equation. It isn't Caesar or any reverence for his memory at work here.
The appearance of Caesar's ghost is a nice touch, but it isn't Caesar or his apparition that loses the war for Brutus and Cassius. The war is lost because Brutus is a terrible military strategist, Cassius is too weak to argue with him, and Pindarus didn't have a pair of binoculars on the battlefield.
Caesar's power ended on the Ides of March with his death. After that, the scramble for power became a jump shot, and Antony grabbed the ball and kept it.