A prescribed performance control (PPC) problem under given constraints for the magnitude and rate of the control signal is considered for uncertain nonlinear relative-degree-one systems affected by external perturbation. In order to solve such task, we propose a robustified version of the well-known Nested Saturation Feedback called Nested Saturation Robust Feedback (NSRF), which: i) simultaneously ensures the predefined transient quality and boundedness by given values of not only magnitude but also rate of the control signal, ii) does not use reciprocal barrier functions (i.e., functions, which grows to infinity whenever its arguments approach some finite limits) in feedback to avoid discontinuities, iii) provides opportunity to chose all control law parameters via solution of a set of linear inequalities by conventional software tools. The theoretical results are validated via an illustrative example.