Tottenham returned to action in a controversy-filled draw with Manchester United on Friday evening.
Jose Mourinho's men drew 1-1 with United, conceding a penalty in the 81st minute which Bruno Fernandes put away.
And what looked for so long like three points could have become none when referee Jon Moss awarded the visitors a penalty in the dying embers when Fernandes went to ground.
The decision was later overturned by VAR, meaning Spurs did indeed take a point and former referee Gallagher agrees with the final call.
"Correct decision," he said on Sky Sports. "I think this is the perfect process of what the VAR is there for. When I first saw it, I actually thought he'd stood on his foot.
"When you inspect it as VAR does, you see that Dier places his foot in the turf and Fernandes actually spins off him.
"I can understand why the ref gave it, but the VAR has done wonderfully well and it's not a penalty."
Gallagher also agreed with Moss' decision to award the first penalty for a foul on Paul Pogba.
"Correct decision - no debate for me," he added.
"If you look, he pushes him with his right arm, and there is quite a significant amount of force.
"There was no need to do it as there was another player covering, but once he did that, he gave Jon Moss no option. It's a spot-on decision."
The result left Tottenham in eighth place and nine points off fourth-place Chelsea.
