Hospital systems play a critical role in treating injuries during disaster emergency responses. Simultaneously, natural disasters hinder their ability to operate at full capacity. Thus, cities must develop strategies that enable hospitals' effective disaster operations. Here, we present a methodology to evaluate emergency response based on a model that assesses the loss of hospital functions and quantifies multiseverity injuries as a result of earthquake damage. The proposed methodology can design effective plans for patient transfers and allocation of ambulances and mobile operating rooms. This methodology is applied to Lima, Peru, subjected to a disaster scenario following a magnitude 8.0 earthquake. Our results show that the spatial distribution of healthcare demands mismatches the post-earthquake capacities of hospitals, leaving large zones on the periphery significantly underserved. This study demonstrates how plans that leverage hospital-system coordination can address this demand-capacity mismatch, reducing waiting times of critically injured patients by factors larger than two.