We report the effect on the phase transitional behavior of 8OCB liquid crystal (LC) doped with functionalized CdSe/ZnS quantum dots (QDs) in different concentrations. The temperature-dependent data of high-resolution optical birefringence and dielectric anisotropy are utilized to characterize the critical anomaly for both the isotropic-to-nematic (I-N) and nematic-to-smectic-A (N-SmA) phase transitions. The obtained results reveal that the order parameter exponent (β) for the pure LC is found to be β=0.249 and does not vary upon the inclusion of QDs in the pure matrix. It describes the weakly first-order characteristic of the I-N phase transition for all the studied samples, which falls within the limit of the tricritical hypothesis. Conversely, depending on the range of the N phase, we observed a nonuniversal nature of the specific heat capacity critical exponent (α^{'}) linked with the N-SmA phase transition for all the studied samples. A relative comparison was made amongst the α^{'} values extracted from both the anisotropy data, and further, a theoretical relationship is established with these exponent values. The coupling strength among the N and SmA order parameters is determined using the optical birefringence data and discussed from the perspective of mutual interaction between the LC-QDs ligands. The results signify that a strong ligand-ligand interaction between neighboring QDs effectively reduces the N range and slightly influences the N-SmA phase transition.