Excitation-energy spectra of C11 nuclei near the η′-meson production threshold have been measured by missing-mass spectroscopy using the C12(p,d) reaction. A carbon target has been irradiated with a 2.5 GeV proton beam supplied by the synchrotron SIS-18 at GSI to produce η′-meson bound states in C11 nuclei. Deuterons emitted at 0 in the reaction have been momentum analyzed by the fragment separator (FRS), used as a high-resolution spectrometer. No distinct structure due to the formation of η′-mesic states is observed although a high statistical sensitivity is achieved in the experimental spectra. Upper limits on the formation cross sections of η′-mesic states are determined, and thereby a constraint imposed on the η′-nucleus interaction is discussed.