Goals from Alex Finney and Jai Reason in extra-time time decided this game and means United will now face League Two opposition in Cheltenham Town, writes Tom Feaheny.
"I have to give credit to Enfield, they performed well in numbers and were dangerous on the break, we had to take our chances, we didn't hence the extra-time, we showed character to get through though," Saunders said to the club's website.
"We created a lot but weren't clinical, I thought we deserved to go through in the end though."
Maidstone are next up against AFC Fylde away from home at the weekend and Saunders knows it will be a tough game.
"We can recover well, I look at Fylde they are a good side, I'm told they are unlucky to be where they are in the league, we will travel up and give it a good go."
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