The Canaries put in a spirited performance against their fancied rivals, who were playing under caretaker manager Freddie Ljungberg for the first time.
"I was not happy with the quality of the decisions in this period of the game," Farke told reporters.
"It felt like each 50:50 call, each duel, each doubtful throw or corner or free kick went against us. The free kick that led to the penalty for me was never a free kick.
"When you speak to the fourth official it is like, 'yes, but it was just a throw in or a corner or a free kick,' but that can change the world in football.
"The penalty was probably the right decision but to replay it was a really strange decision because you will always find something in the rules. Watch the scene back, Max Aarons' foot is outside the box and maybe his knee or a part of an upper body is in the area.
"Arsenal's players were even quicker than him in the box. My feeling is even if he had started 10 inches outside the box it would not have affected the game.
"He would still have cleared it. We were told at the start of the season if you are stood on the six yard line at a penalty then that of course affects the game. Or three yards inside.
"But a part of my player's body was in the box along with Arsenal players.
"The second penalty perhaps (Alex) Lacazette's head was over the line so do you replay that? The second goal we conceded there was another ball on the pitch.
"Should that be allowed? Now don't misunderstand me, that second ball did not affect (Pierre-Emerick) Aubameyang scoring and should have stood but what is the difference?
"To accept one decision against us and not one for us is tough to take. But my lads kept cool in the head to get at least one point."