Functional connectivity using task-residual data capitalizes on remaining variance after mean task-related signal is removed from a time series. The degree of network specificity in language and attention domains featured by task-residual and resting-state data types were compared. Functional connectivity based on task-residual data evidenced stronger laterality of the language and attention connections and thus greater network specificity compared to resting-state functional connectivity of the same connections. Covariance between network nodes of task-residuals may thus reflect the degree to which two regions are coordinated in their specific activity, rather than a general shared co-activation. Task-residual functional connectivity provides complementary data to that of resting-state, emphasizing network relationships during task engagement.