We present new cosmological hydrodynamic simulations that incorporate Dark Matter Annihilation Feedback (DMAF), whereby energy released from the annihilation of dark matter particles through decay channels such as photon or positron-electron pairs provide additional heating sources for local baryonic material. For annihilation rates comparable to WIMP-like particles, we find that the key influence of DMAF is to inhibit gas accretion onto halos. Such diminished gas accretion early in the lifetimes of halos results in reduced gas fractions in smaller halos, and the delayed halo formation times of larger structures, suggesting that DMAF could impact the stellar age distribution in galaxies, and morphology of dwarfs. For a dark matter particle mass of m χ ∼ 10 MeV, there is a 'critical halo mass' of ∼ 10 13 M at z = 0, below which there are large differences when compared to ΛCDM, such as a reduction in the abundance of halo structures as large as 25 percent, reduced gas content by 50 percent and central gas densities reduced down to 10 percent within halos of mass ∼ 10 12 M but with increasing effects in smaller halos. Higher dark matter particle mass models have a smaller 'critical halo mass'. For a m χ ∼ 100 MeV model, we find differences start appearing below halo masses of ∼ 10 12 M and a m χ 1 GeV model, this mass scale lies below the resolution of our simulations, though we still observe changes in the morphology of dwarf galaxies.