Accurate analysis and evaluation of sleep, as well as sleep stage classification, play a crucial role in the diagnosis of sleep disorders and diseases and in the assessment of sleep quality and overall quality of life. However, manual annotation of sleep signals is a time-consuming process and its accuracy strongly depends on the expertise of human scorers. In recent years, intelligent methods have been introduced to automate this process; nevertheless, challenges such as class imbalance among sleep stages—particularly for the N1 stage—still remain. In this study, a sleep stage classification approach with reduced computational complexity is proposed, enabling its application in real-time scenarios and sleep monitoring systems with limited computational resources. In the proposed framework, single-channel EEG signals are employed and transformed into a time–frequency representation so that neural patterns can be analyzed in an image-based form. Subsequently, a convolutional neural network is trained to classify sleep stages without relying on expensive or complex hardware. The objective of this design is to achieve an efficient, lightweight, and practically deployable model suitable for real-world applications, without the need for complex architectures or heavy computational resources. Experimental evaluations demonstrate that, despite its compact structure, the proposed model achieves competitive performance in sleep stage classification, reaching an overall accuracy of 85%. Moreover, the model shows better performance in the challenging N1 stage compared to related studies.