His struggling side were never a match for the Bees, who ensured the victory thanks to a brace from Charlie MacDonald and Myles Weston, and the Gills' poor performance may mark the end of Stimson's spell at Priestfield.
Stimson said: "I don't think it was a 4-0 defeat and I think that at 3-0 if we had taken our chances, then it could have been a different game.
"The players have let themselves down, the club down and me down. Will the chairman stand by me? Who knows?"