Dowman, who is just 15 years old, played a key role in the Gunners' midfield and helped the team in their 3-2 defeat.
Arteta was pleased with Dowman's display and said that he continues to impress with his efficiency and impact on the game.
The manager also compared Dowman's progress to that of Ethan Nwaneri, who made a quick impact in the team last season.
Arteta believes that Dowman has the potential to make his Premier League debut if he continues to perform at this level.