Sleep staging is crucial in assessing sleep quality and diagnosing sleep disorders. Recent advances in deep learning methods with electroencephalogram (EEG) signals have shown remarkable success in automatic sleep staging. However, the use of deeper neural networks may lead to the issues of gradient disappearance and explosion, while the non-stationary nature and low signal-to-noise ratio of EEG signals can negatively impact feature representation. To overcome these challenges, we proposed a novel lightweight sequence-to-sequence deep learning model, 1D-ResNet-SE-LSTM, to classify sleep stages into five classes using single-channel raw EEG signals. Our proposed model consists of two main components: a one-dimensional residual convolutional neural network with a squeeze-and-excitation module to extract and reweight features from EEG signals, and a long short-term memory network to capture the transition rules among sleep stages. In addition, we applied the weighted cross-entropy loss function to alleviate the class imbalance problem. We evaluated the performance of our model on two publicly available datasets, Sleep-EDF Expanded and ISRUC-Sleep, and obtained an overall accuracy rate of 86.39% and 81.97%, respectively, along with corresponding macro average F1-scores of 81.95% and 79.94%. Our model outperforms ex-isting sleep staging models, particularly for the N1 stage, where it achieves F1-scores of 59.00% and 55.53%. The kappa coefficient is 0.812 and 0.766 for the Sleep-EDF Expanded and ISRUC-Sleep datasets, respectively, indicating strong agreement with certified sleep experts. We also investigated the effect of different weight coefficient combinations and sequence lengths of EEG epochs used as input to the model on its performance. Furthermore, the ablation study was conducted to evaluate the contribution of each component to the model's performance.