The correct answer to this open question is the following.
What convinced Inca armies to retreat in their war against the Spanish in 1533 was that the Spaniards killed the Inca Emperor.
We are talking about Atahualpa, the Inca Emperor that was captured by Spanish conqueror Francisco Pizarro, and executed in Augusto 1533. The Spanish troop had better weaponry and horses, an animal never before seen by the Incas. It was so much difficult for the Native Indians to defend against the Spaniards.