We consider general perturbations of a Schwarzschild black holes in the context of f(R) gravity. A reduced set of frame independent master variables are determined, which obey two closed wave equations — one for the transverse, trace-free, tensor perturbations and the other for the additional scalar degree of freedom which characterize fourth-order theories of gravity. We show that for the tensor modes, the underlying dynamics in f(R) gravity is governed by a modified Regge-Wheeler tensor which obeys the same Regge-Wheeler equation as in General Relativity (GR). We find that the possible sources of scalar quasinormal modes (QNMs) that follow from scalar perturbations for the lower multipoles result from primordial black holes, while higher mass, stellar black holes are associated with extremely high multipoles, which can only be produced in the first stage of black hole formation. Since scalar quasinormal modes are short ranged, this scenario makes their detection beyond the range of current experiments.