This paper studies the hierarchical control of uncertain discrete-time nonlinear systems under input constraints. First, the notion of robust approximate simulation relation is defined. We show that by properly designing a control interface, the robust approximate simulation relation can be constructed from a low-complexity, deterministic (abstract) system to the original system. Then, we apply the hierarchical control approach to the robust control synthesis under signal temporal logic specifications. The results show that this approach reduces the computational complexity of the control synthesis, and is in some cases applicable to a larger set of initial states. The effectiveness of the proposed approach is verified by a simulation example.