Given the crucial role of cable-stayed bridges and the challenging environmental conditions they often face, monitoring their health is essential. Stay cables, which are the primary load-bearing elements in cable-stayed bridges, are prone to damage due to environmental conditions. This paper investigated the performance of a method for evaluating the cables of a cable-stayed bridge using deck responses, compared to modal parameters. The technique utilized phase space analysis of deck displacement responses in the time domain under a specific moving load. This method was evaluated through a numerical simulation of the Manavgat cable-stayed bridge. Damage scenarios with intensities of 20%, 30%, and 40% were applied to the cross-sections of the cables. Damage identification was carried out by analyzing the changes in phase space topology (CPST) of the responses between the healthy and damaged models, along with two indicators, the modal assurance criterion (MAC) and modal flexibility. The results showed that the CPST index, unlike modal flexibility, identified the damaged cables at all damage levels except for the back-stay cables. The changes in the modal assurance criterion (MAC) at the 40% damage level were also very insignificant. This method can serve as a preliminary approach for fast and continuous monitoring of cables in cable-stayed bridges, minimizing traffic disruption while relying solely on the displacement responses of the deck.