Recently, deep learning-based classification approaches have made great progress and now dominate a wide range of applications, thanks to their Herculean discriminative feature learning ability. Despite their success, for hyperspectral data analysis, these deep learning based techniques tend to suffer computationally as the magnitude of the data soars. This is mainly because the hyperspectral imagery (HSI) data are multidimensional, as well as giving equal importance to the large amount of temporal and spatial information in the HSI data, despite the redundancy of information in the temporal and spatial domains. Consequently, in literature, this equal information emphasis has proven to affect the classification efficacy negatively in addition to increasing the computational time. As a result, this paper proposes a novel dual branch spatial-spectral attention based classification methodology that is computationally cheap and capable of selectively accentuating cardinal spatial and spectral features while suppressing less useful ones. The theory of feature extraction with 3D-convolutions alongside a gated mechanism for feature weighting using bi-directional long short-term memory is used as a spectral attention mechanism in this architecture. In addition, a union of 3D convolutional neural network (3D-CNN) and a residual network oriented spatial window-based attention mechanism is proposed in this work. To validate the efficacy of our proposed technique, the features collected from these spatial and spectral attention pipelines are transferred to a feed-forward neural network (FNN) for supervised pixel-wise classification of HSI data. The suggested spatial-spectral attention based hyperspectral data analysis and image classification methodology outperform other spatial-only, spectral-only, and spatial-spectral feature extraction based hyperspectral image classification methodologies when compared, according to experimental results.