We report on a study of surface-enhanced infrared absorption (SEIRA) by optical phonons in monolayers (MLs) of CdSe, CdS, and PbS nanocrystals (NCs) deposited on arrays of linear nanoantennas the optimized structural parameters of which allow coupling between the localized surface plasmon resonance (LSPR) and diffraction modes in the far-infrared spectral region. The Langmuir-Blodgett technique was used for homogeneous deposition of the NCs. The structural parameters of the arrays and the NC MLs were determined by scanning electron microscopy. According to the three-dimensional electrodynamic simulations of the electromagnetic field distribution around the antennas, the maximal SEIRA enhancement is realized for an array period of about 15 μm when the energy of a diffraction mode coincides with that of the LSPR mode. SEIRA experimental results are in perfect quantitative agreement with the simulation. The maximal SEIRA enhancement is observed for the nanoantenna length and transverse periodicity predicted by the simulations. The frequency positions of the absorption features indicate that only the NC surface optical phonons are activated in the SEIRA spectra. (Graph Presented).