When asked if he felt his own position was under threat Stimson, who made six changes for the trip to Somerset, said: "Who knows?
"I have always been under pressure. My board has always been spot on with me. They are honest with me because they know I am honest."
Gillingham, who have moved out of the bottom four, should have claimed all three points at Huish Park on Saturday when Curtis Weston rounded goalkeeper Alex McCarthy after 56 minutes but the midfielder hit a post.
Stimson added: "He reacted quickly to get to the rebound but couldn't force the ball in."