Superfluid ^{4}He (He II) is a widely studied model system for exploring finite-size effects in strongly confined geometries. Here, we study He II confined in millimeter-scale channels of 25 and 50 nm height at high pressures using a nanofluidic Helmholtz resonator. We find that the superfluid density is measurably suppressed in the confined geometry from the transition temperature down to 0.6 K. Importantly, this suppression can be accounted for by rotonlike thermal excitations with an energy gap of 5 K. We show that the surface-bound excitations lead to the previously unexplained lack of finite-size scaling of suppression of the superfluid density.