The Gunners fought back from 2-0 down to beat Hull City at Wembley on Saturday and the Spaniard hailed the manager's "brilliant" words at the interval
Goals from James Chester and Curtis Davies gave Steve Bruce's side a shock lead in the showpiece, before Santi Cazorla pulled a goal back to send the Gunners into half-time trailing by a single goal.
Arteta later heaped praise on Wenger, whilst also crediting the fans for their role in the win.
"The manager's speech at half-time was brilliant," the Spaniard told Arsenal's official website. "[He told us] to keep believing in how we should do it and keep performing.
"He told us to stay calm. We had done the most difficult thing, which was to score the first one [after going two down] so now the game was open, we had plenty of time to do it, we could not rush it. It was brilliant, I think the lads continued to play and we showed a lot of experience and composure. I'm really happy, it's a happy day.
"I'm glad overall for the players because they deserve it, for the manager and for the club in general and the fans."
The win ended Arsenal's nine-year trophy drought and Arteta is sure the Gunners fans will not have to wait much longer for more success.
"This club has got every resource to do better than what we've done in the last nine years so hopefully we can build from here," he added.
"We've got some young talent with a lot of experience at their age. So to get through these moments is going to be very important for their careers."