Common damages in concrete materials and structures are usually in small sizes at initial stage, which induce small stiffness and mass loss being difficult to evaluate severity level merely depending on traditional electromechanical admittance (EMA, inverse of impedance) technique. In fact, several state-of-the-art computerized techniques have been incorporated with the EMA for automated evaluation of concrete damages. However, complicated data preprocessing still limits the efficiency of these techniques in terms of accuracy and computational cost. To this end, this paper proposed a novel deep learning approach using one-dimensional (1-D) convolutional neural networks (CNNs) for exploiting the raw EMA signatures to automatically identify tiny damages in concrete structures, which eliminated tedious data preprocessing for network training and testing. Two independent EMA databases measured by smart piezoelectric sensors were established based on proof-of-concept experiment of slight/severe mass-loss damage detection on a concrete cube, as well as practical application of bolt-looseness identification on a full-scaled shield tunnel segment assembled structure. For both tests, effect of varied dimensions of input data on the efficiency of CNN models were evaluated as well. The well-trained CNN model perfectly quantified the severity degrees of mass-loss and bolt-looseness damages, which demonstrated significant superiority than traditional back propagation neural network and the model with less dimensions of input data exhibited higher accuracy. Delightful results in this work potentially provided a potential paradigm of EMA data-driven tiny damage identification for real-life concrete infrastructures.