•A deep learning approach was proposed for electromechanical admittance (EMA)-based damage quantification.•Raw EMA signatures were directly learned by using 2D convolutional neural networks (CNNs).•Input size on the effectiveness of approach was evaluated by developing two CNN models.•Proof of concept experiments were conducted on detecting mass loss damages in concrete structure.•Experimental results confirmed high accuracy and efficiency of the approach to tiny damages. Deep learning approach using convolutional neural networks (CNNs) has ushered in numerous breakthroughs in image-based recognition field, but the electromechanical impedance/admittance (EMI/EMA)-based structural damage identification by CNN remains being refined. This paper proposed a deep learning approach for the raw EMA-based rapid damage quantification on concrete structure utilizing two-dimensional (2D) CNNs. In the approach, the EMA signatures are first split into multiple sub-range responses, among which corresponding to the maximum indices namely root mean square deviations (RMSDs) are selected to construct the input of CNNs for training, and then damage severity degree could be rapidly predicted. The proposed approach is verified through crossover experiments of detecting multiple mass loss damages on a cubic concrete structure. Effect of input size on the performance of the approach is also evaluated by developing different CNN models. Experimental results confirm that the proposed approach is of high accuracy and efficiency even to tiny damages, thus paving a promising way to the real-life monitoring for concrete structures.