Lacazette appeared to be clipped by Christian Kabasele during the early stages of the fixture at the Emirates Stadium, but the Frenchman opted to chase the ball to try to get a shot away before going to ground.
The referee opted against awarding a spot kick, and Gallagher feels that the right decision was reached despite Lacazette looking to stay on his feet.
Gallagher told Sky Sports News: "I was watching this game live and I didn't think it was a penalty, but it's a point which comes back to Matt Jarvis for West Ham all those years ago against Arsenal if a player stops on his feet.
"What I would say in that incident, it is very, very difficult for the referee to give a penalty when he sees Lacazette going after the ball and to shoot like that. If you bring it back, you have given him two chances."
Arsenal netted twice during the closing stages to run out 2-0 winners in North London.