Bukayo Saka put Arsenal in front after his shot went in off Cristian Romero.
Tottenham hit back via Heung-min Son but Arsenal took the lead early in the second half once more via a Bukayo Saka penalty.
Spurs were punished by VAR during Sunday’s north London derby after it intervened to say Cristian Romero had handled a shot by Arsenal defender Ben White.
Following the game, Postecoglou admitted he does not understand the handball rule:
“Mate, I couldn’t see but I’ve got no idea about the handball rule,” he said. “I really don’t.
“I saw the one yesterday at Wolves and it just seems if it hits your hand it’s a penalty and then other times if it hits your hand, it isn’t a penalty. I’ve got no idea.
“It is the one rule in the game I just don’t understand. Unless we start developing armless defenders I don’t know how you are supposed to block things and be in a natural position. It is what it is mate.
“You kind of hope these things even themselves out over the course of a year but I don’t understand the handball rule. I have said that to referees in the past and I don’t know how they see it to be honest.”