Ollie Watkins earned the spot kick early in the second half after going down under a challenge from goalkeeper Bailey Peacock-Farrell, but replays suggested that it was the forward who instigated contact with the Leeds stopper.
However, Gallagher has said that Peacock-Farrell was at fault for giving the referee a decision to make after leading with his legs.
Gallagher told Sky Sports News: "I'm with the referee. I think every referee will give a penalty like that.
"Someone said to me that he is already going down but in that situation, the goalkeeper has come out legs first and he has run the risk. He brought his knees up and gave the referee a decision to make."
Brentford netted from 12 yards but Leeds fought back to salvage a point at Elland Road.