A method for the calculation of the electronic structure of metallic nanoshells is presented. Using this method, we investigate the role of many-electron effects in small nanoshells. A comparison of the electronic properties calculated using Hartree, Hartree-Fock and local density approximations reveals that the Hartree-Fock approximation leads to unphysical results in the same way as it does for bulk electrons in metallic phases. These anomalies disappear with use of the local density approximation, indicating that the effect of correlations is still strong even for very small metallic nanoshells.