Rob Holding handballed in the penalty area but referee Chris Kavanagh did not point to the spot despite appearing to have a clear view.
Holding had already been booked for a bad foul on Kelechi Iheanacho and could have been dismissed over the incident, according to Puel.
Leicester went on to take the lead regardless thanks to Hector Bellerin's own goal, but Mesut Ozil's brilliant individual performance hauled the Gunners to a seventh straight Premier League win.
Puel, though, was clear the Holding handball was a key moment in the game for his Foxes side.
"I am angry about this decision because all the good work from my players was not helped," Puel said to BBC Sport.
"I thought it was a penalty, we saw this from the bench, all the people in the stadium saw this penalty and it was handball.
"It is not possible to have another decision other than a penalty and also it was another yellow card and sending off.
"I didn't speak to the referee afterwards because it is finished and we can't come back with another decision.
"But I regret this decision because all the people in the stadium saw this decision was wrong.
"The penalty is an important thing but also afterwards we needed to score more and be more clinical."