The production of the heavy stable proton-rich isotopes between ^74^Se and ^196^Hg-the p nuclides-is due to the contribution from different nucleosynthesis processes, activated in different types of stars. Whereas these processes have been subject to various studies, their relative contributions to Galactic chemical evolution (GCE) are still a matter of debate. Here we investigate for the first time the nucleosynthesis of p nuclides in GCE by including metallicity and progenitor mass-dependent yields of core-collapse supernovae (ccSNe) into a chemical evolution model. We used a grid of metallicities and progenitor masses from two different sets of stellar yields and followed the contribution of ccSNe to the Galactic abundances as a function of time. In combination with previous studies on p-nucleus production in thermonuclear supernovae (SNIa), and using the same GCE description, this allows us to compare the respective roles of SNeIa and ccSNe in the production of p-nuclei in the Galaxy. The {gamma} process in ccSN is very efficient for a wide range of progenitor masses (13M_{sun}_-25M_{sun}_) at solar metallicity. Since it is a secondary process with its efficiency depending on the initial abundance of heavy elements, its contribution is strongly reduced below solar metallicity. This makes it challenging to explain the inventory of the p nuclides in the solar system by the contribution from ccSNe alone. In particular, we find that ccSNe contribute less than 10% of the solar p nuclide abundances, with only a few exceptions. Due to the uncertain contribution from other nucleosynthesis sites in ccSNe, such as neutrino winds or {alpha}-rich freeze out, we conclude that the light p-nuclides ^74^Se, ^78^Kr, ^84^Sr, and ^92^Mo may either still be completely or only partially produced in ccSNe. The {gamma}-process accounts for up to twice the relative solar abundances for ^74^Se in one set of stellar models and ^196^Hg in the other set. The solar abundance of the heaviest p nucleus ^196^Hg is reproduced within uncertainties in one set of our models due to photodisintegration of the Pb isotopes ^208,207,206^Pb. For all other p nuclides, abundances as low as 2% of the solar level were obtained.