Postecoglou was frustrated to see Romero penalised for blocking Ben White's shot with his hand early in the second half of a thrilling derby at the Emirates Stadium.
Romero had little time to get his hand out of the way as White was close to the Tottenham defender when he unleashed his shot in the six-yard box.
The spot-kick was not given initially, but referee Robert Jones changed his decision after VAR advised him to consult the pitchside monitor.
Bukayo Saka converted the penalty to put Arsenal 2-1 up, but Son Heung-min bagged his second goal of the game to preserve Tottenham's unbeaten start to the Premier League season.
"I've got no idea about the handball rule. I really don't. 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," Postecoglou said.
"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. You kind of hope these things even themselves out over the course of a year but I don't understand the handball rule. I think any clarity would be good."
Prior to the penalty drama, an own goal from Romero in the 26th minute had broken the deadlock, with Tottenham replying through Son's first equaliser from James Maddison's cross.
In his first season with Tottenham after arriving from Scottish champions Celtic, Postecoglou has already revitalised a team that finished last term in disarray.
Toe to toe
Playing with silk and steel in equal measure, they matched their hated neighbours and look capable of pushing for a top four finish.
"It's not about being happy with the result, for me it was about the performance," Postecoglou said.
"You can get a result here, a draw, and like I said before you can walk away knowing that 'you know what, we escaped', but I don't have that feeling now.
"I think we went toe-to-toe with a top team and at times I thought we really asserted our dominance on the game. At times they did but that's what happens when you face top sides."
Arsenal remain unbeaten but boss Mikel Arteta was frustrated his side failed to make it three successive wins in the derby.
Arteta felt the turning point came when Gabriel Jesus won possession from Maddison inside the area, but blazed over the bar with a golden chance to put the Gunners 2-0 ahead.
"We are very disappointed not to earn the three points, that's for sure, and especially when you go in front twice in the game and have the opportunity to win it," he said.
"We had control of the game, could have made it 2-0 with Gabi and then you concede the goal and you have to bounce back. We did and scored the goal but it's a shame that within a minute you concede the other one.
"I think that affected the team emotionally quite a lot and we lacked some composure to make more passes in the final third."
Arteta also leapt to the defence of Jorginho, who was introduced at half-time in place of the injured Declan Rice and lost possession to Maddison in the build-up to Tottenham's second goal.
"Errors are part of football. They're allowed to make errors because they play and we don't play. I love him and we love him," Arteta said.
