Background: Multiple surveys across the globe during the first wave of the pandemic suggested an increase in the prevalence of various psychiatric disorders like depression, anxiety disorder, and insomnia in the general population, patients with acute coronavirus disease-2019 (COVID-19) infection, and in the post-COVID-19 infection patients. However, the data on psychological morbidity during the post-COVID-19 infection phase is limited barring a few small sample size studies. In this background, this study aimed to evaluate the prevalence of neuropsychiatric issues in persons who had suffered from COVID-19 infection and compare the same with persons who did not suffer from COVID-19 infection, but witnessed the same in one of their relatives. Materials and methods: In this cross-sectional web-based study, 1172 adult participants, aged 18–75 years, who had either suffered and recovered from COVID-19 infection or those who did not develop COVID-19 infection but witnessed the infection in a family member completed the PHQ-9, GAD-7 scale, fear of COVID-19 Scale (FCV-19S), brief resilient coping scale (BRCS), brief resilience scale (BRS), and a 19-item self-designed questionnaire to evaluate neuropsychiatric issues and coping mechanisms. Results: In terms of psychiatric morbidity, about one-fourth of those who developed COVID-19 had depression and that of higher severity significantly more than those who did not develop COVID-19 themselves. Similarly, about one-fourth of the persons who developed COVID-19 infection also had anxiety disorder and higher proportion of them had more severe anxiety, which was significantly higher than those who did not develop COVID-19 themselves. Compared to those who did not develop COVID-19 infection themselves, a higher proportion of those who developed COVID-19 demonstrated intense recollection or flashbacks of illness, trying to avoid memories, thoughts, or feelings related to the stressful experience, brain operating slowly, forgetfulness, persistent headache, new-onset seizures, and higher level of resilient coping. Conclusion: There is an urgent need to focus on the mental health consequences of COVID-19 infection and to provide multidisciplinary care to people who have gone through the COVID-19 infection to prevent and manage the post-COVID or long-COVID symptoms.