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Approximate deep neural networks (AxDNNs) are promising for enhancing energy efficiency in real-world devices. One of the key contributors behind this enhanced energy efficiency in AxDNN is the use of approximate multipliers. Unfortunately, the simulation of approximate multipliers does not usually scale well on CPUs and GPUs. As a consequence, this slows down the overall simulation of AxDNNs aimed at identifying the appropriate approximate multipliers to achieve high energy efficiency with a minimum accuracy loss. To address this problem, we present a novel XAI-Gen methodology, which leverages the analytical model of the emerging hardware accelerator (e.g., Google TPU v4) and explainable artificial intelligence (XAI) to precisely identify the non-critical layers for approximation and quickly discover the appropriate approximate multipliers for AxDNN layers. Our results show that XAI-Gen achieves up to 7× lower energy consumption with only 1-2% accuracy loss. We also showcase the effectiveness of the XAI-Gen approach through a neural architecture search (XAI-NAS) case study. Interestingly, XAI-NAS achieves 40% higher energy efficiency with up to 5× less execution time when compared to the state-of-the-art NAS methods for generating AxDNNs.