Since SARS-CoV-2 appeared in late 2019, many studies on the immune response to COVID-19 have been conducted, but the asymptomatic or light symptom cases were somewhat understudied as respective individuals often did not seek medical help. Here, we analyze the production of the IgG antibodies to viral nucleocapsid (N) protein and receptor-binding domain (RBD) of the spike protein and assess the serum neutralization capabilities in a cohort of patients with different levels of disease severity. In half of light or asymptomatic cases the antibodies to the nucleocapsid protein, which serve as the main target in many modern test systems, were not detected. They were detected in all cases of moderate or severe symptoms, and severe lung lesions correlated with respective higher signals. Antibodies to RBD were present in the absolute majority of samples, with levels being sometimes higher in light symptom cases. We thus suggest that the anti-RBD/anti-N antibody ratio may serve as an indicator of the disease severity. Anti-RBD IgG remained detectable after a year or more since the infection, even with a slight tendency to raise over time, and the respective signal correlated with the serum capacity to inhibit the RBD interaction with the ACE-2 receptor.