The Gunners won 2-1, with Arteta throwing Max Dowman and Marli Salmon, both 16, into his starting line-up.
The manager said afterwards, "It was a proper FA Cup game and credit to Mansfield the stadium and the atmosphere the fans created there was a bit of banter.
"They made it really difficult for us. If not, you have to be more ruthless in front of goal than we were today.
"The margin becomes smaller, and you give hope to the opposition. We made a mistake on the goal which cost us the momentum and belief for them. Overall, happy with the performance.
"We have two 16-year-olds in the starting line-up, which I don't think has ever happened, and I am very proud of them.
"I think everyone feels involved. We have the desire that, game by game, we can get closer to the things that we can achieve."