During service, advanced composite materials are susceptible to various forms of damage. Developing an efficient real-time Structural Health Monitoring (SHM) method is of profound significance to ensure the normal operational integrity of the advanced composite structures. This study introduces a novel end-to-end SHM approach employing acoustic emission (AE) techniques and a deep learning model with attention mechanisms (AM) to automate the damage diagnosis process and improve prediction accuracy. Low-velocity impact (LVI) experiments were carried out, recording AE signals for subsequent bi-spectrum analysis. Three dedicated AM-based Convolutional Neural Network (CNN) architectures were designed for damage diagnosis, utilizing 2D bi-spectrum contour images as input data. A comparison was made between the proposed CNN model, deep learning and traditional machine learning models in the context of damage diagnostics, revealing that CNN models combined AM exhibit significantly higher accuracy in pattern recognition tasks. The accuracies of the baseline CNN, self-attention-CNN, multi-head attention-CNN and convolutional block attention module-CNN are 98.22%, 98.50%, 98.85%, and 98.87%, respectively. The CNN embedded with AM demonstrated superior predictive performance and fewer instances of misclassification. Considering the specific demands of damage diagnostics in composite materials, the CBAM-CNN is better suited for composite material health monitoring tasks.