Wenger's side were leading through Per Mertesacker's first half goal when referee Neil Swarbrick ruled that a challenge from Arsenal defender Hector Bellerin on Richarlison was worthy of a penalty.
Television replays suggested Richarlison made the most of minimal contact, but Watford's Troy Deeney stepped up to convert the spot-kick.
Tom Cleverley struck Watford's winner in stoppage-time to hand Arsenal their first defeat in eight games in all competitions.
Gunners boss Wenger was furious with the penalty, saying: "It was a scandalous decision, but what can we do? Nothing.
"You can talk and talk but at the end of the day they scored.
"We had many situations when we could have scored the second and didn't. "After that we were unlucky because the decision on the penalty is a bit ridiculous.
"Then we panicked a bit in the last seconds. We didn't need to give the ball away."
Arsenal trail Premier League leaders Manchester City by nine points and Wenger admitted his side had paid the price for a sloppy second half display.
"We dropped our level in the second half. We lost our fluency, despite that we had the chances to score two or three," he said.