  In the absence of an exact development of the cosmological models based on
the Mashhoon nonlocal gravity, the Newtonian regime clarifies some aspects of
it. To improve this model more reliable, going through some semi-Post-Newtonian
considerations may be useful. One important feature to consider is the
formation of horizons, which can be understood as a consequence of the finite
interaction velocity. This highlights the importance of extending the
integration across the entire space-time, rather than solely focusing on the
spatial sector. In this context, we show that the density of effective dark
matter would increase, while the density of Baryonic matter decreases, during
the deep matter-dominated era. This finding is in contradiction with the
predictions of the standard model of cosmology and it raises concerns about the
compatibility of using Tohline--Kuhn kernel and considering the nonlocal
effects as an effective dark matter in $\Lambda$CDM.
