Biomarkers based on resting-state electroencephalography (EEG) signals have emerged as a promising tool in the study of Alzheimer’s disease (AD). Recently, a state-of-the-art biomarker was found based on visual inspection of power modulation spectrograms where three “patches” or regions from the modulation spectrogram were proposed and used for AD diagnostics. Here, we propose the use of deep neural networks, in particular convolutional neural networks (CNNs) combined with saliency maps, trained on power modulation spectrogram inputs to find optimal patches in a data-driven manner. Experiments are conducted on EEG data collected from fifty-four participants, including 20 healthy controls, 19 patients with mild AD, and 15 moderate-to-severe AD patients. Five classification tasks are explored, including the three-class problem, early-stage detection (control vs. mild-AD), and severity level detection (mild vs. moderate-to-severe). Experimental results show the proposed biomarkers outperform the state-of-the-art benchmark across all five tasks, as well as finding complementary modulation spectrogram regions not previously seen via visual inspection. Lastly, experiments are conducted on the proposed biomarkers to test their sensitivity to age, as this is a known confound in AD characterization. Across all five tasks, none of the proposed biomarkers showed a significant relationship with age, thus further highlighting their usefulness for automated AD diagnostics.