Brain dynamics recorded via electroencephalography (EEG) is conceptualized as a sum of two components - "phase-locked" and "non-phase-locked" to the stimulus. Phase-locked activity is often implicitly studied as Event-Related Potentials (ERPs), and the trial-averaged estimates - evoked potentials (EP) considered both time-locked and phase-locked to the stimulus. The non-phase-locked activity, on the other hand, refers to an increase in power in a narrow band or broadband frequencies in the signal emerging at variable phases from stimulus initiation. Both components are understood to stem from different neuronal mechanisms; hence, accurately characterizing them is of immense importance to neuroscientific studies. Here, we discuss the drawbacks of currently used methods to separate the phase-locked and non-phase-locked activity and propose a novel Concurrent Phaser Method (CPM) that simultaneously decomposes the two components. First, we establish that the single-trial separation of phase-locked and non-phase-locked power is an ill-posed problem. Second, using simulations where ground truth validation is possible, we elucidate how the estimation of non-phase-locked power gets biased by phase-locked power in the state-of-the-art averaging method and ways to resolve the issue using CPM. Next, we use two experimental EEG datasets - audio oddball and auditory steady-state responses (ASSR) to show that empirical signal-to-noise estimates warrant the usage of CPM to separate phase-locked and non-phase-locked activity. Thus, using ground truth validation from simulations and demonstration in real experimental scenarios, the efficacy of the proposed CPM is established.