Les Gones were twice forced to come from behind during the game in New Jersey, with Bafetimbi Gomis and Jimmy Briand cancelling out John Utaka's stunning opener and a penalty from Emanuel Herrera respectively, before clinching victory courtesy of a 4-2 shoot-out success.
Garde felt that referee Jorge Gonzalez's decision to penalise Mouhamadou Dabo for handling a free-kick from Marco Estrada struck had been the decisive moment in the game.
"I think there were several elements to explain the differences [in Lyon's performance level] between the two halves," the former Arsenal man mused during his post-match press conference on Saturday night.
"The first half was a case of there being some emotion and I think we didn't play in a liberated fashion. I asked my players at half-time to play with more freedom and to try to attack.
"The second half started with an injustice, with the referee giving Montpellier a penalty which I don't feel should have been [given]. But that stimulated my players and got them playing together more and going forward together.
"I also think there was a physical aspect and we finished the game more strongly than Montpellier."
Garde, who was capped seven times by France, took charge of Lyon last summer, succeeding Claude Puel as coach.