Felipe Anderson's opener came after Pablo Zabaleta was found on the right flank in an offside position, while the full-back could have been adjudged to have pushed Marcus Rashford in the build-up to West Ham's third goal.
However, Gallagher has claimed that it was difficult for either the assistant or referee to award free kicks to the visitors in both situations at the London Stadium.
Regarding the first goal, Gallagher told Sky Sports News: "It was very difficult to tell with the naked eye. The assistant is in exactly the right position and the distance between Zabaleta and [Victor] Lindelof is half of the width of the field.
"When you look at it, his kneecap is offside. If he had given it offside, you would then be saying that he has guessed. I think in that situation, he can't be sure that he is offside so he keeps his flag down."
On the third effort, Gallagher added: "I didn't think it was a foul. The game goes on, no-one thinks about it, but as we have said many, many times, it is the consequence of the decision with the ball going in the net so it becomes a talking point."
West Ham went on to register a 3-1 victory in East London.