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The influence of the Dzyaloshinskii–Moriya interaction (DMI) on the eigenmodes of magnetic nanostructures is attracting interest for both fundamental reasons and prospects in applications. In this study, the characteristics of spin waves eigenmodes in either long stripes or elliptical dots magnetized in-plane, with lateral dimensions of the order of 100 nm, are analyzed by micromagnetic simulations in presence of a sizeable DMI. Using the GPU-accelerated software MuMax3, we show that the eigenmodes spectrum is appreciably modified by the DMI-induced non-reciprocity in spin-waves propagation: the frequencies of the eigenmodes are red-shifted and their spatial profiles appreciable altered due to the lack of stationary character in the direction orthogonal to the magnetization direction. As a consequence, one finds a modification of the expected cross-section of the different modes in either ferromagnetic resonance or Brillouin light scattering experiments, enabling one to detect modes that would remain invisible without DMI. In this respect, the modifications of the spectrum can be directly connected to a quantitative estimation of the DMI constant. Moreover, it is seen that for sufficiently large values of the DMI constant, the low-frequency odd eigenmode changes its profile and becomes soft, reflecting the transition of the ground state from uniform to chiral.