This work deals with the double excitation of electronic states of semiconductor quantum dots as induced by photoabsorption. The prime focus is put on the manifestation of quantum size and correlation effects in the two-particle excited spectrum. The photon field is treated within the dipole approximation whereas the Green function method is employed to describe the excited two-particle spectrum. Our numerical simulations demonstrate that the dimensionality of the dot as well as the amount of inter-electronic correlation have a marked effect on the dot's excitation spectrum. The underlying physics of these effects can be understood from the functional structure of the inter-electronic interaction in a many-electron system as well as from the characteristic change of the electronic states when varying the size of the dot from the strong localization regime to an extended structure.