Mild cognitive impairment (MCI) is a state that falls between the more severe decline of dementia and the typical aging-related loss of memory and thinking. MCI must be diagnosed earlier to avoid complete memory loss. Several Machine Learning (ML) and Deep Learning (DL) models employ standard feature extraction approaches to achieve effective MCI categorization. However, it has some drawbacks, including lower accuracy, longer time consumption, less feature learning, and increased model complexity. The proposed method introduces a novel deep learning model to address the limitations of existing MCI classification approaches. Initially, the Electroencephalography (EEG) signal is pre-processed using the Sequential Savitzky-Golay filtering model (SEQ-SG), which improves the signal's quality and removes unnecessary noise. The Improved Tuneable Q Wavelet Transform (ITQWT) feature extraction model is used to extract relevant features. The Coati Stochastic Optimization (CSO) algorithm selects the most optimal channel features from the EEG signal. Finally, the proposed deep learning model, Dual Attention Assisted Compact Convolutional Network with Stacked Bi-LSTM (DCCN-SBiL), is used to classify EEG signals into three categories: Alzheimer's disease, MCI, and normal. The proposed model is optimized using the Gazelle Optimization Algorithm (GOA), which tunes the classification model's hyper- parameters. The proposed classification model is evaluated using the Mendeley Dataset, which contains EEG signals from Alzheimer's disease, MCI and Normal. The proposed model has shown great performance in many performance parameters, including 97.25% accuracy, 95.94% recall, 96.03% precision, and 94.65% specificity in MCI classification.