The literature on COVID-19 continues to increase daily. Cognitive sequelae associated with COVID-19 infection still draw the attention of the scientific community given the lack of consensus about their existence, etiology, characterization and reversibility. The aim of this study is to provide a neuropsychological identikit for younger (<65 years) and older (≥65 years) individuals diagnosed with COVID-19 infection, at baseline and after 3 and 6 months. In total, 226 individuals took part in a retrospective observational study and their cognitive performance was compared across groups (younger adults vs. older adults) and time (T0, T1, T2). The results highlighted differences between younger and older adults in the Montreal Cognitive Assessment (MoCA) global score, as expected in consideration of the different physiological conditions of the two populations. However, memory performance highlighted the two groups as characterized by a difference in patterns of recall that may move beyond a physiological explanation and provide information about COVID-19 cognitive sequelae. This study suggests that cognitive deficits observed in COVID-19 survivors may reflect a difficulty in attention and concentration that interferes mainly with retrieval processes. This result fits well with the concept of “brain fog” typical of post-COVID-19 syndrome and may also reflect the stress experienced while facing the pandemic.