The visitors looked set to earn a hard-fought draw at Emirates Stadium, only for match official Bobby Madley to penalise Jose Fonte for making contact with substitute Olivier Giroud inside the area during second-half stoppage time.
Southampton, who remain winless after four matches of the new Premier League season, also saw spot-kicks awarded against them in an away defeat to Manchester United and home draw with Sunderland in recent weeks.
"It's very hard for my players, very hard," Puel told the BBC. "It's a third penalty in four games. It's easier against us to [award] a penalty.
"A big disappointment for my players. A draw would have been [logical] this afternoon."
Asked if he felt Madley made the wrong decision, Puel said: "It's difficult. For me, the two players play the ball. It's very hard after the 90 minutes to take this penalty.
"I don't want to say anything about the referee. It's not in my spirit. It's a big disappointment for all the work [we did] on the ground. You can win this game."
Saints begin their Europa League group stage campaign at home to Sparta Prague next week, Puel calling for his squad to focus after a painful outcome in north London.
"We go now to another game on Thursday and it's important to keep the concentration," he said.
"But it's interesting for the future because we are strong in defence. With good players on the pitch … it's a positive. But in four games, you aren't rewarded - this is difficult to accept."
Puel, who lost out to his former boss at Monaco in Arsenal manager Arsene Wenger, acknowledged his team afforded their hosts too much space after the break.
"We can win the game two or three times … it's important to believe," he said.
"Second half you move back a little … too much, because we were playing against a good team in Arsenal. We lost the ball quickly, it's important to keep the ball."