Coherent perfect absorption (CPA) describes the absence of all outgoing modes from a lossy resonator, driven by lossless incoming modes. Here, we show that for nanoresonators that also exhibit radiative losses, e.g., plasmonic nanoantennas, a generalized version of CPA (gCPA) can be applied. In gCPA outgoing modes are suppressed only for a subset of (guided plasmonic) modes while other (radiative) modes are treated as additional loss channels - a situation typically referred to as perfect impedance matching. Here we make use of gCPA to show how to achieve perfect impedance matching between a single nanowire plasmonic waveguide and a plasmonic nanoantenna. Antennas with both radiant and subradiant characteristics are considered. We further demonstrate potential applications in background-free sensing.