We present a study on the gamma-ray emission detected by the AGILE-GRID from the region of the SNR G78.2+2.1 (Gamma Cygni). In order to investigate the possible presence of gamma rays associated with the SNR below 1 GeV, it is necessary to analyze the gamma-ray radiation underlying the strong emission from the pulsar PSR J2021+4026, which totally dominates the field. An off-pulse analysis has been carried out, by considering only the emission related to the pulsar off-pulse phase of the AGILE-GRID light curve. We found that the resulting off-pulsed emission in the region of the SNR - detected by the AGILE-GRID above 400 MeV - partially overlaps the radio shell boundary. By analyzing the averaged emission on the whole angular extent of the SNR, we found that a lepton-dominated double population scenario can account for the radio and gamma-ray emission from the source. In particular, the MeV-GeV averaged emission can be explained mostly by Bremsstrahlung processes in a high density medium, whereas the GeV-TeV radiation by both Bremsstrahlung (E < 250 GeV) and inverse Compton processes (E > 250 GeV) in a lower density medium.