The optical response of CdSe semiconductor nanocrystals is investigated using the reduced single-electron density matrix in real space, calculated by means of the time-dependent Hartree-Fock technique. The spectroscopic signatures of exciton confinement are analyzed using the frequency-dependent electronic coherence matrix (off-diagonal density-matrix elements). The effects of Hartree and the Fock (exchange) type Coulomb interactions on the exciton binding energy are discussed. The latter result in almost dark excitons situated energetically below the main transition. Off-diagonal Coulomb matrix elements lead to larger exciton binding energies compared with previous calculations, and result in a better agreement of the size dependence of the lowest optical transition with experiment.