Assessment of the depth of anesthesia (DOA) primarily relies on electroencephalogram (EEG) signals. However, the high dimensionality of EEG data can increase computational complexity and limit real-time clinical applications. An efficient EEG signal representation is therefore important for practical DOA monitoring. We propose a compact statistical EEG representation that summarizes each one-second EEG segment using a set of descriptors: the mean, standard deviation, maximum, minimum, median, and the first and third quartiles (Q1 and Q3). The resulting representation, together with the electromyogram (EMG) signal, is fed into a hybrid deep learning model that combines a residual neural network (ResNet) variant with a bidirectional long short-term memory (Bi-LSTM) layer and an attention mechanism. Comparative experiments were conducted using both raw EEG signals and the proposed compact representation, and the model’s performance was benchmarked against state-of-the-art approaches. The proposed approach achieved a root mean square error (RMSE) of 5.99 ± 1.10 and an accuracy of 83.73%, outperforming several of these methods and remaining comparable to the strongest baselines, with its clearest advantage in computational efficiency: it attained the lowest inference latency among all evaluated models (1.91 ms per sample on CPU), together with substantially reduced training time and memory usage. K-fold cross-validation confirmed consistent generalization across data partitions. The combination of the compact statistical EEG representation and the hybrid deep learning model predicts DOA with competitive accuracy at low computational cost. These results indicate that the method is a promising and computationally efficient solution for real-time anesthesia monitoring.