Brain imaging has provided a useful tool to examine the neural processes underlying human cognition. A critical question is whether and how task engagement influences the observed regional brain activations. Here we highlighted this issue and derived a neural measure of task engagement from the task-residual low-frequency blood oxygenation level-dependent (BOLD) activity in the precuneus. Using independent component analysis, we identified brain regions in the default circuit - including the precuneus and medial prefrontal cortex (mPFC) - showing greater activation during resting as compared to task residuals in 33 individuals. Time series correlations with the posterior cingulate cortex as the seed region showed that connectivity with the precuneus was significantly stronger during resting as compared to task residuals. We hypothesized that if the task-residual BOLD activity in the precuneus reflects engagement, it should account for a certain amount of variance in task-related regional brain activation. In an additional experiment of 59 individuals performing a stop signal task, we observed that the fractional amplitude of low-frequency fluctuation (fALFF) of the precuneus but not the mPFC accounted for approximately 10% of the variance in prefrontal activation related to attentional monitoring and response inhibition. Taken together, these results suggest that task-residual fALFF in the precuneus may be a potential indicator of task engagement. This measurement may serve as a useful covariate in identifying motivation-independent neural processes that underlie the pathogenesis of a psychiatric or neurological condition.