Developing optimal controllers for aggressive high speed quadcopter flight remains a major challenge in the field of robotics. Recent work has shown that neural networks trained with supervised learning are a good candidate for real-time optimal quadcopter control. In these methods, the networks (termed G\&CNets) are trained using optimal trajectories obtained from a dynamical model of the quadcopter by means of a direct transcription method. A major problem with these methods is the effects of unmodeled dynamics. In this work we identify these effects for G\&CNets trained for power optimal full state-to-rpm feedback. We propose an adaptive control strategy to mitigate the effects of unmodeled roll, pitch and yaw moments. Our method works by generating optimal trajectories with constant external moments added to the model and training a network to learn the policy that maps state and external moments to the corresponding optimal rpm command. We demonstrate the effectiveness of our method by performing power-optimal hover-to-hover flights with and without moment feedback. The flight tests show that the inclusion of this moment feedback significantly improves the controller's performance. Additionally we compare the adaptive controller's performance to a time optimal Bang-Bang controller for consecutive waypoint flight and show significantly faster lap times on a 3x4m track.