A novel neuro adaptive control framework for discrete-time multivariable nonlinear uncertain systems is developed. The proposed framework is Lyapunov-based and guarantees, instead of ultimate boundedness, partial asymptotic stability of the closed-loop system; that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. Unlike standard neural network approximation, we assume that the approximation error can be confined in a small gain-type norm-bounded conic sector over a compact set. This helps to couple tools from robust control with adaptive laws in discrete time to prove partial asymptotic stability of the closed-loop system. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.