We investigate the electron correlation in few‐electron closed‐shell atomic systems and similarly in few‐electron quantum dots under weak confinement. As usual we start with restricted Hartree–Fock (HF) calculations and add electron correlation in steps in a series of approximations based on the single particle Green's function approach: (i) second‐order Green function (GF); (ii) 2ph‐Tamm‐Dancoff approximation (TDA); and (iii) an extended version thereof which introduces ground‐state correlation into the TDA. Our studies exhibit similarities and differences between weakly confined quantum dots and standard atomic systems. The calculations support the application of HF, GF, and TDA techniques in the modeling of three‐dimensional quantum dot systems. The observed differences emphasize the significance of confinement and electronic features unique to quantum dots, such as the increased binding of electrons with higher angular momentum and thus—compared to atomic systems—modified shell‐filling sequences.