Background: Cognitive complaints are among the most frequent symptoms of post-acute sequelae of COVID-19 (PASC). This study aimed to investigate the frequency, characteristics, and clinical correlates of cognitive complaints (CC) in PASC, particularly in relation to objective neuropsychological (NP) performance. Methods: Seventy-four participants underwent psychiatric, medical, and NP testing approximately 7 months after acute COVID-19. The Patient Assessment of Own Functioning Inventory (PAOFI) was used to characterize the frequency and severity of CC in domains of memory, language, and cognitive/executive function. The associations of CC with sociodemographic, medical, psychiatric, and NP variables were assessed utilizing correlational analysis, logistic regression, and pairwise comparisons of those categorized as having CC vs. not having CC. Results: Taken together, approximately one-third of the study participants had clinically significant CC. Memory difficulty was the most frequent CC, although all categories were frequently endorsed. Memory and cognitive/executive complaints correlated with NP tests in these and multiple other NP domains. CC were more likely to be under-reported in those with diminished NP performance than over-reported in those without diminished performance. Acute COVID-19 symptom severity, elevated depressive symptoms, and NP tests of diminished attention and psychomotor processing speed were independent predictors of CC in logistic regression. Conclusions: Cognitive complaints after acute COVID-19 should be taken seriously, as they are likely to reflect diminished NP performance, as well as medical, psychiatric, and functional burdens. However, patients with PASC may not accurately identify or characterize objective cognitive difficulties, so programs offering comprehensive care for patients with PASC should offer formal neuropsychological testing.