The quest to improve the density, speed and energy efficiency of magnetic memory storage has led to the exploration of new ways of optically manipulating magnetism at the ultrafast time scale, in particular in ferrimagnetic alloys. While all-optical magnetization switching is well-established on the femtosecond timescale, lateral nanoscale confinement and thus the potential significant reduction of the size of the magnetic element remains an outstanding challenge. Here we employ resonant electromagnetic energy funneling through plasmon nanoantennas to influence the demagnetization dynamics of a ferrimagnetic TbCo alloy thin film. We demonstrate how Ag nanoring-shaped antennas under resonant optical femtosecond pumping reduce the overall demagnetization in the underlying films up to three times compared to non-resonant illumination. We attribute such a substantial reduction to the nanoscale confinement of the demagnetization process. This is qualitatively supported by the electromagnetic simulations that strongly evidence the resonant optical energy-funneling to the nanoscale from the nanoantennas into the ferrimagnetic film. This observation is an important step for reaching deterministic ultrafast all-optical magnetization switching at the nanoscale in such systems, opening a route to develop nanoscale ultrafast magneto-optics.