Neutron stars are known to be efficient accelerators producing particles with ultra-relavistic energies. As a by product they also emit copiously photons from radio wavelengths up to gamma-rays. As a follow up of our previous work on particle acceleration simulation near neutron stars, in this paper, we discuss the impact of radiation reaction on test particles injected into their magnetosphere. We therefore neglect the interaction between particles through the electromagnetic field as well as gravitation. We found that while due solely to the Lorentz force electrons reach Lorentz factors up to $\gamma=10^{14}$ and protons up to $\gamma=10^{10.7}$, when radiation reaction is enabled electrons reach energies up to $\gamma=10^{10.5}$ and protons up to $\gamma=10^{8.3}$. The latter values are more realistic since the radiation reaction feedback is predominant within the magnetosphere. Moreover, as expected, symmetrical behaviours between the north and the south hemispheres is highlighted, either with respect to the location around the neutron star or with respect to particles of opposite charge to mass ratio~$q/m$. Consequently, it is useless to simulate the full set of geometrical parameters to get an overview of all possibilities. The study of the influence of the magnetic dipolar moment inclination shows similar behaviours whether or not radiation reaction is switch on: protons (respectively electrons) impact less the surface of the neutron star as the inclination angle increases (decreases for electrons) while if the rotation and magnetic axes are aligned, all the protons impact onto the neutron star, and all the electrons impact the surface if the rotation and magnetic axes are anti-aligned. Similarly, we still find that particles can be ejected away from the neutron star, with preferred directions, were it for the number of particles or for their Lorentz factors