The human sensorimotor system can adapt to various changes in the environmental dynamics by updating motor commands to improve performance after repeated exposure to the same task. However, the characteristics and mechanisms of the adaptation process remain unknown for dexterous manipulation, a unique motor task in which the body physically interacts with the environment with multiple effectors, i.e., digits, in parallel. We addressed this gap by using robotic manipulanda to investigate the changes in the digit force coordination following mechanical perturbation of an object held by tripod grasps. As the participants gradually adapted to lifting the object under perturbations, we quantified two components of digit force coordination. One is the direction-specific manipulation moment that directly counteracts the perturbation, whereas the other one is the direction-independent internal moment that supports the stability and stiffness of the grasp. We found that trial-to-trial improvement of task performance was associated with increased manipulation moment and a gradual decrease of the internal moment. These two moments were characterized by different rates of adaptation. We also examined how these two force coordination components respond to changes in perturbation directions. Importantly, we found that the manipulation moment was sensitive to the extent of repetitive exposure to the previous context that has an opposite perturbation direction, whereas the internal moment did not. However, the internal moment was sensitive to whether the post-change perturbation direction was previously experienced. Our results reveal, for the first time, that two distinct processes underlie the adaptation of multi-digit force coordination for dexterous manipulation.