Speaking on Sky Sports News, Gallagher highlighted an example during Super Sunday's Chelsea v Hull game where a Branislav Ivanovic header was acrobatically saved by Allan McGregor.
Replays showed the ball had not crossed the line - a fact that was communicated immediately to referee Jon Moss after his GDS wrist watch failed to vibrate.
"It was so, so close," said Gallagher. "It would have been difficult for the assistant to give it as the ball was in mid-air and there were so many bodies between him and the goal.
"We all knew it didn't go in because the referee's watch didn't go off - and it killed it there and then. There was no chance for the players to surround the ref and claim it was in.
"It was over and done with, it was a weight off the referee's mind, there was no comeback from the players and the game carried on.
"The key thing is when the ball is just across the line and it triggers the referee's watch - I think that's when everyone will say 'that's brilliant' and it will have been shown to have worked.
"But this example has already shown what a good system it is."