With the classical ensemble model, we investigate the manifestations of the Coulomb tail of electron-electron interaction in nonsequential double ionization by comparing the results from the short-range electron-electron interaction with those from the Coulombic electron-electron interaction. At the intensity below the recollision threshold, the two-electron momentum distributions in the direction parallel to the laser polarization show an anticorrelated behavior for the Coulombic electron-electron interaction while a correlated behavior for the short-range interaction, which indicates the responsibility of the Coulomb tail of the electron-electron interaction for the experimentally observed anticorrelated emission [Y. Liu, S. Tschuch, A. Rudenko, M. Durr, M. Siegel, U. Morgner, R. Moshammer, and J. Ullrich, Phys. Rev. Lett. 101, 053001 (2008)]. In the transverse direction, for the Coulombic electron-electron interaction, the two electrons exhibit no effect of repulsion at an intensity below the recollision threshold while a strong repulsion effect at an intensity above the threshold, which becomes weaker as the laser intensity further increases. Back analysis shows that the role of the Coulomb tail of electron-electron interaction leads asymmetric energy sharing (AES) to be prevalent at recollision. This AES results in the two electrons leaving the ion at different times or with different initial momenta, which is responsible for the anticorrelated behavior in the parallel direction and the intensity-dependent repulsion effect in the transverse direction.