After City prevailed by a 2-1 scoreline at Old Trafford, United boss Jose Mourinho suggested that Ander Herrera deserved to be awarded a penalty after an alleged foul by Nicolas Otamendi, rather than receive a yellow card for diving.
Gabriel Jesus also appeared fortunate to avoid a booking for simulation during the first half, but Gallagher feels that Oliver got both decisions correct, going on to describe his performance as "a masterclass".
On Herrera, Gallagher told Sky Sports News: "If you watch the incident, Herrera goes over his own foot and Otamendi doesn't move. It's got to be deliberate, and it's quite clearly not a deliberate trip. For me, I think it was quite clearly not a penalty.
On Jesus, he added: "This is absolutely right. Michael Oliver was on his game right from the start - it was a masterclass. [It's not a yellow] because there was a little bit of contact.
"We have to be careful with a number of simulation acts over the last few weeks, and what we're looking to do is punish the ones which are clear acts of simulation. There is contact, but it's not a penalty. The player goes into him. It's similar to the Herrera one."