The design of output constrained control system for unmanned aerial vehicles deployed in confined areas is an important issue in practice and not taken into account in many autopilot systems. In this study, the authors address a neural networks-based adaptive trajectory tracking control algorithm for multi-rotors systems in the presence of various uncertainties in their dynamics. Given any sufficient smooth and bounded reference trajectory input, the proposed algorithm achieves that (i) the system output (Euclidean position) tracking error converges to a neighbourhood of zero and furthermore (ii) the system output remains uniformly in a prescribed set. Instead of element-wise estimation, a norm estimation approach of unknown weight vectors is incorporated into the control system design to relieve the onboard computation burden. The convergence property of the closed-loop system subject to output constraint is analysed via a symmetric barrier Lyapunov function augmented with several quadratic terms. Simulation results are demonstrated on a quadrotor model to validate the effectiveness of the proposed algorithm.