Many attempts have been made to fully explore flexibility, resistance to corrosion, and processing advantage of epoxy resin filled with carbon nanotubes (CNTs) as conductive filler, although sometimes with a certain degradation of polymers’ intrinsic properties. It is important to move the percolation threshold into the region of smaller CNTs’ concentration. The results of a broadband dielectric investigation of multiwalled CNT (MWCNT)/epoxy resin composites in wide temperature range from room temperature to 450 K were analyzed for percolation. Far below the percolation threshold (0.25 wt. % MWCNT) the dielectric properties of the composite are mostly determined by alpha relaxation in pure polymer matrix and the freezing temperature decreases due to the extra free volume at the polymer–filler interface. Close to the percolation threshold, the composite shows the negative temperature coefficient effect in the temperature region, where the pure polymer matrix becomes conductive. The activation energy of DC conductivity increases with the MWCNT concentration far below the percolation threshold and decreases close to it (1.5 wt. % MWCNT). The dielectric analysis of the MWCNT/epoxy resin reveals a significant influence of the polymer matrix on the temperature dependence of composite dielectric properties.