In this paper, an alternative perspective for the generation of millimetric high-gradient resonant plasma waves is discussed. This method is based on the plasma-wave excitation by energetic single-cycle THz pulses whose temporal length is comparable to the plasma wavelength. The excitation regime discussed in this paper is the quasi-nonlinear regime that can be achieved when the normalized vector potential of the driving THz pulse is on the order of unity. To investigate this regime and determine the strength of the excited electric fields, a Particle-In-Cell (PIC) code has been used. It has been found that by exploiting THz pulses with characteristics currently available in laboratory, longitudinal electron plasma waves with electric gradients up to hundreds MV/m can be obtained. The mm-size nature of the resonant plasma wave can be of great utility for an acceleration scheme in which high-brightness electron bunches are injected into the wave to undergo a strong acceleration. The long-size nature of the acceleration bucket with respect to the short length of the electron bunches can be handled in a more robust manner in comparison with the case when micrometric waves are employed.