In the hypothesis that the majority of bright TeV sources detected by H.E.S.S. are powered by pulsar activity, like, e.g., pulsar wind nebulae (PWN) or TeV halos, we estimate the main properties of the Galactic pulsar population. We obtain a constraint on the spin-down time $\tau_{\rm sd}$, the initial period $P_{0}$ and the magnetic field $B_{0}$. Evaluating the cumulative flux expected at Earth by the considered population, we show that unresolved PWNe contribute to the Galactic gamma-ray diffuse emission in the whole high-energy range from GeV to PeV. In particular, at TeV energy, their contribution could be as significant as $40\%$ of the gamma emission due to resolved sources. We argue that unresolved PWNe could have also important implications for the interpretation of Fermi-LAT and Tibet AS$\gamma$ diffuse flux determinations in the GeV and sub-PeV energy domains.