Here, we explore theoretically the concept of enhanced directivity from electrically small subwavelength radiators containing negative-parameter materials, such as plasmonic materials with negative permittivity at THz, infrared and optical frequencies. In particular, we study higher order plasmonic resonances of a subwavelength core-shell spherical nano-antenna, and we analyze the near-zone field distributions and far-field radiation patterns of such a structure when it is excited by a small dipole source, demonstrating analytically and numerically the possibility of having highly directive patterns from a nano-structure with electrically small dimensions. Radiation characteristics and intrinsic limitations on performance are analyzed in detail, and a potential application of this novel technique for super-resolution detection of the displacement of a nano-object is also pointed out.