The Gunners needed Ebere Eze's second-half winner to edge the fifth round tie 2-1.
Mansfield striker Rhys Oates said afterwards: "Before the game, the gaffer said 'Just have a go. We were not expected to win the game, so have a go and enjoy it'.
"We created more chances than we thought we could, and we have given them a game.
"I had a few chances. I feel like I could have put one away myself. The players they have got they are going to make good interceptions. You just have to keep going."It was a dream come true. I said as a child I wanted to play for Arsenal or against Arsenal and I have managed to do that now."
Mansfield goalscorer Will Evans also stated, "I wanted to prove a point today - not just to the team but to myself as well. It's typical isn't it, for me to have a league goal drought and then come on for a half against Arsenal and have a goal against them.
"Games come thick and fast. We are onto the next game. So you don't really have much time to take it all in. One day, I might just go through my old goals and enjoy them. But we got a shift again on Tuesday night (against Reading)."