Background: Perception of exertion is essential for self-regulation in sports. The ability to rate perceived exertion (RPE) is regarded as psychophysiological competence, although cognitive components of RPE are largely unknown. The present study tested the hypothesis that cognitive processing speed, perseveration and figural fluency correlate with RPE. Methods: The present study tested relationships between the performance in neuropsychological tests and the competence for RPE assessed during soccer training in 30 adults with and 22 adults without intellectual disabilities. Results: Mean correlation coefficients for RPE and heart rate differed significantly between participants with intellectual disabilities (r = 0.41) and participants without intellectual disabilities (r = 0.71). The variance of RPE could be partially explained by neuropsychological performance measures reflecting cognitive processing speed and perseveration and by age. Conclusions: The results point to an impaired perception of exertion in people with intellectual disabilities, which can be partially explained by individual neuropsychological competencies.