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Weak vibrational signals in the infrared and terahertz spectral region can be enhanced by orders of magnitude when employing the electromagnetic near fields of plasmonic nanostructures. This approach is known as antenna-assisted surface-enhanced infrared absorption (SEIRA) and allows for a broad range of possible sensing applications. In the present work, we investigate the scaling of the SEIRA enhancement with wavelength, particularly towards the molecular fingerprint region (500 to 1500 cm^-1). We apply the concept of SEIRA to perform resonant antenna-enhanced spectroscopy of molecules in a spectral range from 4.5 to 45 THz (6.6 to 67.5 µm wavelength, 148 to 1500 cm^-1) using a standard Fourier transform infrared spectrometer. We fabricate arrays of rectangular gold antennas by electron-beam lithography and coat them with 30 nm thick layers of the fullerenes C₆₀ and C₇₀, respectively. For the single digit THz measurements, we utilize spin-coated amino acids, particularly threonine. The resonances of the structures are tailored to spectrally match the molecular absorption features. An increased SEIRA enhancement of two orders of magnitude is found for antennas resonant at 6.7 THz when compared to 45 THz, corresponding to a λ³ scaling over a frequency range of one order of magnitude. This scaling behavior is in excellent agreement with both numerical simulations and classical antenna theory. Further increase towards the single-digit THz region will yield the potential for ultrasensitive THz spectroscopy.