Quantum dots (QDs) are significant fluorescent materials for energy transfer studies with phthalocyanines (Pcs) and phthalocyanine (Pc)-like biomolecules (such as chlorophylls). Carbon-based QDs, especially, have been used in numerous studies concerning energy transfer with chlorophylls, but the numbers of studies concerning energy transfer between phthalocyanines and carbon-based QDs are limited. In this study, peripherally, hydroxythioethyl terminal group substituted metal-free phthalocyanine (H2Pc) and zinc phthalocyanine (ZnPc) were noncovalently (electrostatic and/or pi-pi interaction) attached to carbon QDs containing boron and nitrogen to form QD-Pc nanoconjugates. The QD-Pc conjugates were characterized using different spectroscopic techniques (Fourier transform infrared spectroscopy and transmission electron microscopy). The absorption and fluorescence properties of QD-Pc structures in solution were studied. It was found that the quantum yields of the QDs slightly decreased from 30% to 25% upon doping the QDs with heteroatoms B and N. Forster resonance energy transfer efficiency was calculated as 33% for BCN-QD/ZnPc. For the other conjugates, almost no energy transfer from QDs to Pc cores was observed. It was shown that the energy transfer between QDs to Pc cores was completely different from the energy transfer between QDs and photosynthetic pigments, and therefore we concluded that heteroatom doping in the QD structure and the existence of zinc metal in the phthalocyanine structure is obligatory for an efficient energy transfer.