The resonant break-up of 19 C on protons measured at RIKEN [Phys. Lett. B 660, 320 (2008)] is analyzed in terms of a valence-core model for 19 C including possible core excitations. The analysis of the angular distribution of a prominent peak appearing in the relative-energy spectrum could be well described with this model and is consistent with the previous assignment of 5/2 + for this state. Inclusion of core-excitation effects are found to be essential to give the correct magnitude of the cross section for this state. By contrast, the calculation assuming an inert 18 C core is found to largely underestimate the data.