The Hurst exponent (H) isolated in fractal analyses of neuroimaging time-series is implicated broadly in cognition. The connection between H and the mathematics of criticality makes it a candidate measure of individual differences in cognitive resource allocation. Relationships between H and multiple mental disorders have been detected, suggesting that H is transdiagnostically associated with psychopathology. Here, we demonstrate a gradient of decreased H with increased general psychopathology and attention-deficit/hyperactivity extracted factor scores during a working memory task which predicts concurrent and future working memory performance in 1,839 children. This gradient defines psychological and functional axes which indicate that psychopathology is associated with an imbalance in resource allocation between fronto-parietal and sensory-motor regions, driven by reduced resource allocation to fonto-parietal regions. This suggests the hypothesis that impaired cognitive function associated with psychopathology follows from a reduced cognitive resource pool and a reduction in resources allocated to the task at hand.