The Premier League champions were deserved 2-0 victors in Sunday's fixture at the Emirates Stadium, but City could have conceded a spot kick during the second half.
Gallagher told Sky Sports News: "I think if Michael [Oliver] sees the pictures we see, he would give a penalty because there are two issues for me. Mendy doesn't look at the ball, he isn't interested in the ball and he grabs hold of the player to haul him down. But as the ball came to [Granit] Xhaka in front, Michael only sees him out of the corner of his eye and he can't be sure whether it is a foul.
"It's easy for us but at that point, it's not so easy for the referee because he has so much to concentrate on. I think this shows why there were so many penalties given at the World Cup because more was seen, more was picked up and more was relayed back to the referee to look at himself."
Mendy also provided assists for both goals in the match in North London.