The Voyager 2 crossing of the termination shock indicated that most of the upstream energy from the thermal solar wind ions was transferred to pickup ions (PUIs) and other energetic particles downstream of the shock. We use hybrid simulations at the termination shock for the Voyager 2, flank, and tail directions to evaluate the distributions of different ion species downstream of the shock over the energy range of 0.52–55 keV. Here, we extend the work of Gkioulidou et al., which showed an energy-dependent discrepancy between modeled and energetic neutral atom (ENA) observations, and fit distributions to a hybrid model to show that a population of PUIs accelerated via diffusive shock acceleration (DSA) to become low-energy anomalous cosmic rays (ACRs) can bridge the gap between modeled and observed ENA fluxes. Our results with the inclusion of DSA via hybrid fitting give entirely new and novel evidence that DSA at the termination shock is likely to be an important physical process. These ACRs carry a significant fraction of the energy density at the termination shock (22%, 13%, and 19% in the Voyager 2, flank, and tail directions, respectively). Using these ACRs in global ENA modeling of the heliosphere from 0.52 to 55 keV, we find that scaling factors as large as 1.8–2.5 are no longer required to match ENA observations at energies of ∼1–4 keV. Large discrepancies between modeled and observed ENAs only remain over energies of 4–20 keV, indicating that there may be a further acceleration mechanism in the heliosheath at these energies.