With the Saints leading 2-1 heading into the closing minutes, Doucoure bundled the ball into the net to earn Watford a share of the spoils at Vicarage Road.
Replays showed that Southampton were right to feel aggrieved with the decision, but Gallagher has defended East and his assistant over the incident.
Gallagher told Sky Sports News: "The referee, I believe, is the victim here because he has no chance whatsoever. If you look where the player's head is, he moves his head forward, and the only person who can clearly see that that is handball is the goalkeeper.
"When you look at it sideways on, when you see the head go forward you cannot be sure at that distance whether he has headed it or not. The only person who knows is the player himself and obviously the goalkeeper."
The result of Saturday's game left Southampton just one point above the relegation zone in the Premier League standings.