Properties of the inner heliosheath (IHS) plasma are inferred from energetic neutral atom (ENA) observations by ~1 au spacecraft. However, the Compton–Getting effect due to the plasma velocity relative to the spacecraft is rarely taken into account, even though the plasma speed is a significant fraction of the ENA speed. In this study, we transform Interstellar Boundary Explorer (IBEX) ENA spectra to the IHS plasma frame using flow profiles from a 3D heliosphere simulation. We find that proton spectra in the plasma frame are steeper by ~30% to 5% at ~0.5 to 6 keV, respectively, compared to ENAs in the spacecraft frame. While radial plasma flows contribute most to the Compton-Getting effect, transverse flows at mid/high latitudes and the heliosphere flanks account for up to ~30% of the frame transformation for IBEX-Hi at ~0.7 keV and up to ~60% for IBEX-Lo at ~0.1 keV. We determine that the majority of IHS proton fluxes derived from IBEX-Hi measurements in 2009–2016are statistically consistent with power-law distributions, with mean proton index ~2.1 and standard deviation ~0.4. We find significantly fewer spectral breaks in IBEX observations compared to early analyses, which we determine were a product of the "ion gun" background prevalent in ~2009–2012 before corrections made by McComas et al. in subsequent data releases. We recommend that future analyses of the IHS plasma utilizing ENA measurements take into account the Compton-Getting effect including radial and transverse flows, particularly IBEX and Interstellar Mapping and Acceleration Probe measurements below ~10 keV.