The extragalactic background light (EBL) contains all the radiation emitted by nuclear and accretion processes in stars and compact objects since the epoch of recombination. Measuring the EBL density directly is challenging, especially in the near-to-far-infrared wave band, mainly due to the zodiacal light foreground. Instead, gamma-ray astronomy offers the possibility to indirectly set limits on the EBL by studying the effects of gamma-ray absorption in the very high energy (VHE: >100 GeV) spectra of distant blazars. The High Altitude Water Cherenkov Gamma Ray Observatory (HAWC) is one of the few instruments sensitive to gamma rays with energies above 10 TeV. This offers the opportunity to probe the EBL in the near/mid-IR region: λ = 1-100 μm. In this study, we fit physically motivated emission models to Fermi-LAT gigaelectronvolt data to extrapolate the intrinsic teraelectronvolt spectra of blazars. We then simulate a large number of absorbed spectra for different randomly generated EBL model shapes and calculate Bayesian credible bands in the EBL intensity space by comparing and testing the agreement between the absorbed spectra and HAWC extragalactic observations of two blazars. The resulting bands are in agreement with current EBL lower and upper limits, showing a downward trend toward higher wavelength values λ > 10 μm also observed in previous measurements.