This paper addresses the problem of almost disturbance decoupling with internal stability (ADD) for inherently nonlinear systems with uncontrollable unstable linearization. Although achieving an arbitrary small level of disturbance attenuation in the sense of the L₂-gain is usually impossible by smooth state feedback, we show that there exists a non-smooth but continuous state feedback control law, yielding a closed-loop system which is globally strongly stable in the absence of disturbance, and in the presence of disturbance, whose L₂-gain between the disturbance input and the system output is less than or equal to an arbitrarily small positive number γ > 0. In contrast to the existing results in the literature, all the growth conditions imposed previously to achieve ADD via smooth state feedback are completely removed under this continuous feedback framework, enabling one to deal with a significantly larger class of nonlinear systems.