Background/Objectives: Beyond respiratory problems, COVID-19 can cause a variety of symptoms, such as neurological disorders caused by biological and psychological factors. Brain fog (BF), a post-illness cognitive impairment that many patients report, can be evaluated with reaction time (RT) testing. Response latency is measured by RT, which can be either simple (sRT) or complex (cRT). This study focuses on how COVID-19 affects cognitive function, with particular attention on RT changes, BF prevalence, and implications for daily life. Methods: The study included 599 participants from Bosnia and Herzegovina, Croatia and Serbia. RT was measured using PsyToolkit and participants completed a COVID-19-associated BF questionnaire. Participants who experienced BF after their latest COVID-19 infection rated its severity using a visual analogue scale (VAS). Additional clinical data were obtained from medical records. Results: BF was reported by 40% of participants post-COVID-19. Men reported it less frequently but found it more disruptive. RT progressively declined post-infection, reaching peak impairment at 15 weeks, following recovery, with RT normalizing by six months. Conclusions: COVID-19 is linked to temporary RT impairment, peaking at 15 weeks post-infection and resolving by six months, independent of BF presence. This study emphasizes the need for a biopsychosocial approach to BF management. Easily available RT assessments should be incorporated into routine clinical practice.