This article investigates the impact of addition various types of nanoparticles with different structural, dimensional, and morphological properties on the interphase region formed between the particle/matrix and the curing behavior of the epoxy affect the nanocomposite material properties. For this purpose, epoxy nanocomposites (NCs) were produced by adding multi-walled carbon nanotube (MWCNT) and alumina (Al2O3) nanoparticles (NPs) into the epoxy matrix at different rates (0.5–2.0 wt.%). The effects of the particle/matrix interaction on the properties of the composite have been revealed by chemical, thermal, mechanical analyzes and microstructure investigations. An increase in the absorption density, which reveals the physical interaction of nanoparticles with the epoxy matrix, was observed in Fourier-transform infrared spectroscopy. Absorption vibration peak intensities in nanocomposite samples were at most 1.0 wt.% Al2O3 and 1.25 wt.% CNT added nanocomposites. It was observed that the Tg value increased depending on the number of nanoparticles. The addition of Al2O3 increased Tg values more than CNT. Besides, the mechanical properties of NCs were determined by tensile tests. The highest increase in mechanical properties was achieved by adding 1.25 wt.% CNT and 1.0 wt.% Al2O3, respectively. Mechanical properties tended to decrease at higher addition rates. The shape, size, amount, and distribution of nanoparticles added into the epoxy matrix directly affected the NCs' properties. It has been determined that homogeneously dispersed spherical Al2O3 nanoparticles are more effective than fiber-shaped CNTs in the properties of NCs.