We present a simple scheme of narrowband terahertz (THz) generation by optical rectification in the lithium niobate crystal covered by a binary phase mask. It is shown that a single-domain crystal illumination by spatiotemporal shaped fs-laser pulses is equivalent to the formation of a transversally patterned, quasi-phase-matching structure. Decrease of the optical beam size on the mask leads to an increase of the THz-wave linewidth from 17 GHz to a few THz. The frequency of the generation was tuned in the range of 0.4-1.0 THz by building images of the mask in the crystal with various magnifications. Application results of the presented THz source for measuring transmittance of the superconducting NbN thin film in the 4.2-15 K temperature range are also presented.