Background: The health emergency caused by COVID-19 revealed the shortcomings of health services (HS), but little is known about how this has impacted the mental health of health professionals (HP) when perceiving these difficulties. Methods: Data were collected through an online survey administered to HP in Lima (Peru) between May and July 2020. A questionnaire was applied to identify perceived quality of health services (PHQS). A network analysis was performed, and the centrality measures of the variables were calculated and plotted. Results: A total of 507 HP completed the survey. In the network analysis of PHQS, four clusters were identified: (A) “empathy” and “recognition of competencies,” (B) “logistical support,” “protection,” “personal early diagnosis,” and “early family diagnosis”; C) “professional competence with regard to their treatment and treatment for their family,” “equipment for their treatment and treatment for their family,” “professional competence with regard to their treatment and treatment for their family,” and “institutional support for them and their family”; and D) “fear of being infected or infecting their family,” “fear of dying or death of a family member,” “knowledge stability,” “job burnout,” and “role change.” The variables of PHQS with the greatest centrality were “equipment for their treatment,” “equipment for the treatment of their family,” and “early family diagnosis.”. Conclusions: The structure of the PHQS of HP describes direct and indirect influences of different variables in the context of COVID-19.