The prediction of mechanical elastic response of laminated hybrid polymer composites with basic carbon nanostructure, that is carbon nanotubes and graphene, inclusions has gained importance in many advanced industries like aerospace and automotive. For this purpose, in the current work, a hierarchical, four-stage, multilevel framework is established, starting from the nanoscale, up to the laminated hybrid composites. The proposed methodology starts with the evaluation of the mechanical properties of carbon nanostructure inclusions, at the nanoscale, using advanced 3D spring-based finite element models. The nanoinclusions are considered to be embedded randomly in the matrix material, and the Halpin-Tsai model is used in order to compute the average properties of the hybrid matrix at the lamina micromechanics level. Then, the standard Halpin-Tsai equations are employed to establish the orthotropic elastic properties of the unidirectional carbon fiber composite at the lamina macromechanics level. Finally, the lamination theory is implemented in order to establish the macroscopic force-strain and moment-curvature relations at the laminate level. The elastic mechanical properties of specific composite configurations and their performance in different mechanical tests are evaluated using finite element analysis and are found to considerably increase with the nanomaterial volume fraction increase for values up to 0.5. Further, the hybrid composite structures with graphene inclusions demonstrate better mechanical performance as compared to the identical structures with CNT inclusions. Comparisons with theoretical or other numerical techniques, where it is possible, demonstrate the accuracy of the proposed technique.