This study focuses on entropy based analysis of EEG signals for extracting features for a neural network based solution for identifying anesthetic levels. The process involves an optimized back propagation neural network with a supervised learning method. We provided the extracted features from EEG signals as training data for the neural network. The target outputs provided are levels of anesthesia stages. Wavelet analysis provides more effective extraction of key features from EEG data than power spectral density analysis using Fourier transform. The key features are used to train the Back Propagation Neural Network (BPNN) for pattern classification network. The final result shows that entropybased feature extraction is an effective procedure for classifying EEG data.