This work introduces a self-supervised neuro-analytical, cost efficient, model for visual-based quadrotor control in which a small 1.7M parameters student ConvNet learns automatically from an analytical teacher, an improved image-based visual servoing (IBVS) controller. Our IBVS system solves numerical instabilities by reducing the classical visual servoing equations and enabling efficient stable image feature detection. Through knowledge distillation, the student model achieves 11x faster inference compared to the teacher IBVS pipeline, while demonstrating similar control accuracy at a significantly lower computational and memory cost. Our vision-only self-supervised neuro-analytic control, enables quadrotor orientation and movement without requiring explicit geometric models or fiducial markers. The proposed methodology leverages simulation-to-reality transfer learning and is validated on a small drone platform in GPS-denied indoor environments. Our key contributions include: (1) an analytical IBVS teacher that solves numerical instabilities inherent in classical approaches, (2) a two-stage segmentation pipeline combining YOLOv11 with a U-Net-based mask splitter for robust anterior-posterior vehicle segmentation to correctly estimate the orientation of the target, and (3) an efficient knowledge distillation dual-path system, which transfers geometric visual servoing capabilities from the analytical IBVS teacher to a compact and small student neural network that outperforms the teacher, while being suitable for real-time onboard deployment.