  Recent observations of the diffuse Galactic \gr emission (DGE) by the {\it
Fermi} Large Area Telescope ({\it Fermi}-LAT) have shown significant
deviations, above a few GeV until about 100 GeV, from DGE models that use the
GALPROP code for the propagation of cosmic ray (CR) particles outside their
sources in the Galaxy and their interaction with the target distributions of
the interstellar gas and radiation fields. The surplus of radiation observed is
most pronounced in the inner Galaxy, where the concentration of CR sources is
strongest. The present study investigates this "{\it Fermi}-LAT Galactic Plane
Surplus" by estimating the \gr emission from the sources themselves, which is
disregarded in the above DGE models. It is shown that indeed the expected hard
spectrum of CRs, still confined in their sources (SCRs), can explain this
surplus. The method is based on earlier studies regarding the so-called EGRET
GeV excess which by now is generally interpreted as an instrumental effect. The
contribution from SCRs is predicted to increasingly exceed the DGE models also
above 100 GeV, up to \gr energies of about ten TeV, where the corresponding
surplus exceeds the hadronic part of the DGE by about one order of magnitude.
Above such energies the emission surplus should decrease again with energy due
to the finite life-time of the assumed supernova remnant sources. Observations
of the DGE in the inner Galaxy at 15 TeV with the Milagro \gr detector and, at
TeV energies, with the ARGO-YBJ detector are interpreted to provide
confirmation of a significant SCR contribution to the DGE.
