The Gunners captain played a starring role on Saturday, scoring an emphatic double as the Gunners came from behind to secure Arteta a major trophy just eight months into his first role as a manager.
Victory crucially ensures Arsenal qualify for the Europa League next season, having missed out domestically with an eighth-placed Premier League finish.
Prior to the game, Arteta provided assurances that Aubameyang - who has been linked with a move away from the Emirates with less than one year remaining on his contract - would stay on beyond the cup final.
The Spaniard also believed an FA Cup win would help convince the 31-year-old to stay - a sentiment he asserted once more after the final whistle.
"He [Aubameyang] knows what I think about him, I want to build a squad around him," Arteta told the BBC. "I want him to stay, it is about getting the deal done.
"I think moments like that will help him to believe we are on the right path and he is a big part of it. He is loved by everyone at the club. I think he will [stay]."
The Spaniard also praised Arsenal's immense spirit at Wembley after falling behind to an early Christian Pulisic goal and revealed his pride upon qualifying for Europe.
"It was a difficult start when we conceded so early," he added. "If I know something about these players, is that we weren't going to give up.
"We played probably the best 30 minutes after since I arrived. I am so proud to represent these players and this club.
"It is a double reward for us. It is really important for this club in every way to be in Europe. We all did it so I am so happy.
"The players were completely knackered and they made a massive effort through the coronavirus to keep fit, so I am so happy for them."