Acoustic-hydrodynamic feedbacks are a common theme in jet noise. Strong sound emissions are supported by fluid instabilities, whose core is not necessarily localized in space. A common example is the feedback-loop instability of cavity flows, impinging jets or the flow past airfoils. The feedback-loop is composed of a convective instability, which is usually an instability of the shear layer, and an acoustic pressure wave or a hydrodynamic nonlocal effect. Despite the fact that such a mechanism is widely accepted, a precise identification of the most sensitive spatial regions underpinning the instability is missing. Herein, we propose a non-local decomposition of the structural sensitivity, which allows us to precisely identify the most sensitive regions of the flow responsible for the closure of the feedback-loop. The systematic use of these techniques could be applied in the design of passive flow control devices.