As for Shakespeare's Antony, I would have to say yes, he is responsible for his fall.
At the beginning of the play, he is ruler of one third of the fledgling Roman Empire. He is "stationed" so to speak in Egypt. Although he is married, it is no secret that he is having an affair with Cleopatra.
When his wife dies, it opens the door for the couple but because of the political situation, he marries Octavius's sister, Octavia. This does not stop the affair.
Foolishly Antony listens to the queen and instead of fighting the invading Roman forces on land where he has proved to be an excellent field command, he meets them at sea which proves to be disastrous.
Antony made some very bad decisions, but he made them and he is responsible for the result. In the end, he had no other choice but to fall on his sword.