Anomalous, or “excitonic” mean values (EMV) corrections to the Coulomb repulsion effects on electronic and electron-phonone characteristics of the epitaxial single-layer and carbine are studied. It is demonstrated that in-plane and in-chain EMV correction to the nearest neighbor electron hopping energy is small, while for the Coulomb interaction between these nanostructures and metallic substrate can be significant. This conclusion can be applied to some other carbon nanostructures. •The role of the anomalous “excitonic” mean values (EMV) in the interatomic Coulomb repulsions is studied.•Account of EMV is significant for the graphene - substrate coupling but plays small role for the in-plane coupling in graphene.•The general results obtained for graphene are also qualitatively valid for the epitaxial carbyne.