The champions and runners-up from the previous two campaigns were involved in a highly entertaining, yet controversial, contest at the Etihad Stadium.
Despite playing with a man advantage for the second half, City only scrambled a 2-2 draw against the Gunners through a 98th-minute equaliser from John Stones.
Both Pep Guardiola and Mikel Arteta were left frustrated with some of the decisions made by Oliver, the latter furious that Leandro Trossard was handed a second yellow card for kicking the ball away.
After committing a foul on Bernardo Silva, Trossard was deemed to have halted the resumption of play by booting the ball away from the action.
What did Gallagher have to say?
There were just 0.84 seconds between Oliver's whistle being blown and Trossard kicking the ball away, yet Gallagher feels that the Belgian playmaker and his manager can have no complaints.
Speaking on Sky Sports News' 'Ref Watch' programme, Gallagher said: "No [there can be no complaints], because it's a foul, there's no doubt about that. Would the player have have kicked the ball away like that if there was no foul and pause in play?
"Most certainly not because he's not going to pass to [Gabriel} Martinelli like that. I feel for him because he's gone to pull out but the damage is already done.
"We've already seen it earlier this season that referees are very hard on it this season. He should know better than to do it. The referees have said they'll be hard and fast on it. You could show me one or two where they've got away, but by and large, referees have been very strong on this.
"If one player gets away with it, it's not justification for another player to say 'I'm being punished'."
Was Doku lucky?
From Arsenal's perspective, there is an argument that Jeremy Doku could have been cautioned for a similar infringement, but Gallagher did not see it that way.
He added: "I do not think this is kicking the ball away and delaying the restart. The free kick is in the wrong place. Michael Oliver is trying to move it back. Doku looks at the referee, and then toes it back to an Arsenal player to take a free kick.
"I don't think that's delaying the restart. That's passing the ball back. It's a massive difference."
Stones' last-gasp leveller meant that City were able to end the week at the top of the Premier League table, Arsenal sitting in fourth position.