In this paper, we explore a way to extract the Zernike coefficients from low-resolution PSF images using a neural network model. The goal of this study is to obtain accurate reconstructions of instrumental responses even with under-sampled PSFs. We used the Python module POPPY to simulate a Newtonian telescope system with a primary mirror diameter of 1 meter and a secondary mirror diameter of 0.2 meter. PSFs were simulated over a wavelength range from 200 nm to 1000 nm. Detector sampling parameters included a pixel scale of 0.05 arcseconds/pixel and a 32x32 pixel grid. The ZerNet model was developed based on the Inception architecture. The input is a 32x32 pixel PSF image and the output is a set of Zernike coefficients. The model has three blocks of convolutional kernels of different sizes. These are combined and flattened, then pass through several layers of dense neurons before being activated by a hyperbolic tangent function to predict Zernike coefficients. The model was trained using the Adam optimizer with a learning rate of 0.001 over 40 epochs and a batch size of 64. The data was divided into three sets: training (70%), validation (20%), and test (10%). The ZerNet model showed good accuracy in predicting Zernike coefficients from PSF images. The accuracy improved with increasing wavelength, reaching 95.34% at 1000 nm. The PSF reconstruction error was measured using the Frobenius norm and showed a reduction in error with higher order Zernike coefficients. The model showed that the median error decreased with increasing order, proving that including higher order Zernike coefficients helps with PSF reconstruction.