This study presents a machine learning-aided approach to accurately estimate the region of attraction (ROA) of a multi-rotor unmanned aerial vehicle (UAV) controlled using a linear quadratic regulator (LQR) controller. Conventional ROA estimation approaches rely on a nominal dynamic model for ROA calculation, leading to inaccurate estimation due to unknown dynamics and disturbances associated with the physical system. To address this issue, our study utilizes a neural network to predict these unknown disturbances of a planar quadrotor. The nominal model integrated with the learned disturbances is then employed to calculate the ROA of the planer quadrotor using a graphical technique. The estimated ROA is then compared with the ROA calculated using Lyapunov analysis and the graphical approach without incorporating the learned disturbances. The results illustrated that the proposed method provides a more accurate estimation of the ROA, while the conventional Lyapunov-based estimation tends to be more conservative.