In his first start of the season, Dowman, 16, scored twice as a heavily rotated Arsenal beat Ipswich 4-2 at Portman Road to reach the League Cup fourth round.
It was the type of performance that will undoubtedly see his already high stock raise even higher, something Arteta is hoping to temper.
Speaking to Sky Sports after the game, Arteta was full of praise for the youngster, but he won’t be throwing him in at the deep end just yet.
"Very happy with a lot of aspects, the way we played, to maintain the momentum, some individual performances were really good so in general a really good night," he said.
On Max Dowman: "Max was brilliant. Some actions made the difference and were outstanding. We know the talent and we have to look after him. The environment around him is really good so step by step.
"He is only 16 years old and we have to be careful. We don't want to stop him, but we need to develop him. We're fully aware of what he needs and he will have full opportunities to play."