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 provides additional heating sources for local baryonic material. For annihilation rates comparable to weakly interacting massive particle (WIMP)-like particles, we find that the key influence of DMAF is to inhibit gas accretion on to haloes. Such diminished gas accretion early in the lifetimes of haloes results in reduced gas fractions in smaller haloes, 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(chi) similar to 10 MeV, there is a 'critical halo mass' of similar to 10(13) M-circle dot at z = 0, below which there are large differences when compared to Lambda cold dark matter, such as a reduction in the abundance of halo structures as large as 25 per cent, reduced gas content by 50 per cent and central gas densities reduced down to 10 per cent within haloes of mass similar to 10(12) M-circle dot but with increasing effects in smaller haloes. Higher dark matter particle mass models have a smaller 'critical halo mass'. For a m(chi) similar to 100 MeV model, we find differences start appearing below halo masses of similar to 10(12) M-circle dot and a m(chi) greater than or similar to 1 GeV model, this mass scale lies below the resolution of our simulations, though we still observe changes in the morphology of dwarf galaxies.