  Millisecond Pulsars are second most abundant source population discovered by
the Fermi-LAT. They might contribute non-negligibly to the diffuse emission
measured at high latitudes by Fermi-LAT, the IDGRB. Gamma-ray sources also
contribute to the anisotropy of the IDGRB measured on small scales by
Fermi-LAT. We aim to assess the contribution of the unresolved counterpart of
the detected MSPs population to the IDGRB and the maximal fraction of the
measured anisotropy produced by this source class. We model the MSPs spatial
distribution in the Galaxy and the gamma-ray emission parameters by considering
radio and gamma-ray observational constraints. By simulating a large number of
MSPs populations, we compute the average diffuse emission and the anisotropy
1-sigma upper limit. The emission from unresolved MSPs at 2 GeV, where the peak
of the spectrum is located, is at most 0.9% of the measured IDGRB above 10
degrees in latitude. The 1-sigma upper limit on the angular power for
unresolved MSP sources turns out to be about a factor of 60 smaller than
Fermi-LAT measurements above 30 degrees. Our results indicate that this
galactic source class represents a negligible contributor to the high-latitude
gamma-ray sky and confirm that most of the intensity and geometrical properties
of the measured diffuse emission are imputable to other extragalactic source
classes. Nevertheless, given the MSP distribution, we expect them to contribute
significantly to the gamma-ray diffuse emission at low latitudes. Since, along
the galactic disk, the population of young Pulsars overcomes in number the one
of MSPs, we compute the gamma-ray emission from the whole population of
unresolved Pulsars in two low-latitude regions: the inner Galaxy and the
galactic center.
