City had already taken a 1-0 lead when the referee gave the visitors a spot kick for a foul on Raheem Sterling by goalkeeper Hugo Lloris, but replays showed that the infringement had taken place outside of the box.
However, Gallagher has defended the decision of Jon Moss by claiming that the official had to make the call without the advice of his assistant.
Gallagher told Sky Sports News: "It's easy to see on the replay that the foul is outside the box. It's a difficult call in full speed for both the referee and the assistant.
"My first reaction was to look at the assistant to see if he could aid the referee but when you look across he can't see past the defenders. The referee will say he was certain it was a penalty as he won't give one that involves doubt."
City eventually emerged victorious by a 3-1 scoreline at Wembley Stadium.