We present a low-temperature scanning tunneling spectroscopy study of the local density of states (LDOS) on the (12110)-surface of the decagonal quasicrystal d–Al–Ni–Co and the (100)-surface of its structurally closely related approximant Y–Al–Ni–Co in the range of ±1 eV around the Fermi energy. The LDOS of both surfaces are dominated by a large parabolic pseudogap centered at the Fermi energy, which can be attributed to the Hume–Rothery stabilization mechanism or to an orbital hybridization. Superimposed on this large pseudogap, a spatially varying fine structure is revealed, whose spatial distribution correlates with the structures of both of the surfaces. This fine structure shows narrow peaks and pseudogaps exhibiting typical energy widths between 50 and 150 meV. The spatial extent of these localized states is of the order of the width of the topographic features, which is about 0.45 nm. Our findings show that specific electronic states are localized on equivalent topographic features regardless of the presence of periodic or quasiperiodic long-range order. We interpret this result as an indication that the fine structure in the LDOS is dominated much more by the complex short-range order than by the presence of the quasiperiodic long-range order.