We report a study of the infrared response by localized surface plasmon resonance (LSPR) modes in gold micro- and nanoantenna arrays with various morphologies and surface-enhanced infrared absorption (SEIRA) by optical phonons of semiconductor nanocrystals (NCs) deposited on the arrays. The arrays of nano- and microantennas fabricated with nano- and photolithography reveal infrared-active LSPR modes of energy ranging from the mid to far-infrared that allow the IR response from very low concentrations of organic and inorganic materials deposited onto the arrays to be analyzed. The Langmuir-Blodgett technology was used for homogeneous deposition of CdSe, CdS, and PbS NC monolayers on the antenna arrays. The structural parameters of the arrays were confirmed by scanning electron microscopy. 3D full-wave electromagnetic simulations of the electromagnetic field distribution around the micro- and nanoantennas were employed to realize the maximal SEIRA enhancement for structural parameters of the arrays whereby the LSPR and the NC optical phonon energies coincide. The SEIRA experiments quantitatively confirmed the computational results. The maximum SEIRA enhancement was observed for linear nanoantennas with optimized structural parameters determined from the electromagnetic simulations. The frequency position of the feature's absorption seen in the SEIRA response evidences that the NC surface and transverse optical phonons are activated in the infrared spectra.