The Cherenkov Telescope Array is the next generation of observatory using imaging air Cherenkov technique for very-high-energy gamma-ray astronomy. Its first prototype telescope is operational on-site at La Palma and its data acquisitions allowed to detect known sources, study new ones, and to confirm the performance expectations. The application of deep learning for the reconstruction of the incident particle physical properties (energy, direction of arrival and type) have shown promising results when conducted on simulations. Nevertheless, its application to real observational data is challenging because deep-learning-based models can suffer from domain shifts. In the present article, we address this issue by implementing domain adaptation methods into state-of-art deep learning models for Imaging Atmospheric Cherenkov Telescopes event reconstruction to reduce the domain discrepancies, and we shed light on the gain in performance that they bring along.