[en] Excitons in two-dimensional nanomaterials are studied by solving the many-electron Hamiltonian with a configuration-interaction approach. It is shown that graphene or phosphorene nanoflakes can not accommodate any excitonic bound states if the long-range Coulomb interaction is suppressed when the systems are placed in a high-k dielectric environment or on a metal substrate. Hence it is revealed that an electron–hole pair created by an optical excitation does not always form an exciton even in a confined nanostructure. The negative exciton binding energy is found to exhibit distinct dependence on the strength of short-range Coulomb interaction as the system undergoes a phase transition from non-magnetic to anti-ferromagnetic. It is further shown that the electron–hole pair may form an exciton state only when the long-range Coulomb interaction is recovered in the nanoflakes. (paper)