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After a goalless first half, Callum Maycock gave the hosts the lead right at the start of the second half, but we hit back 25 minutes later through Evan Mooney.
Both sides pushed for a winner in the closing stages, but it was our young Gunners who prevailed thanks to another late, decisive moment from Emerson Nwaneri, who netted an 87th-minute winner to send us through.
"I'm really proud of the players," Horseman said on the performance, "we were quite young, we had three 16-year olds playing, fully deserved, and then the under-21s had a bit of a tough one on Saturday.
"So to come to a place like this against a very good team, and then obviously the physical mismatches that these games produce, I'm really proud to get the win.
"I think it was fully deserved, I thought we played really well, created a lot of chances, but in some ways it feels better because we had to come from behind. So it's a massive achievement for the players, and I'm really proud of them tonight."
The result sees us progress to the last 32 of the competition regardless of the result in the final game between Barnet and Leyton Orient, although we could jump up to top spot if the O's inflict a heavy defeat on the group-leading Bees.
Either way, Horseman said our young Gunners will look forward to their first knockout tie, with the competition a difficult one for under-21s sides historically.
"Look, you want to win every game, but traditionally in this competition, not just Arsenal, [it's difficult]. I think West Ham were the only ones last year to qualify, they were quite an old team.
"So for us to do it, particularly after the start against Barnet, where obviously we barely had a back four in place, and to lose 5-1, is brilliant.
"We've gone away to two League 1 teams and won 2-1, and to play in the stadiums against proper league players in a game that you have to win, I think we've just got to keep giving them as many [of these games as possible]."
With the group stages successfully navigated, we'll be back in EFL Trophy action in December.
While a date for the draw is yet to be confirmed, Horseman is hoping to bring his squad together to find out who we'll face for a place in the last 16.
"It's something to really, really look forward to. It's uncharted territory for Arsenal and most under-21s teams.
"I'm not sure when the draw is, but when [the details] come out, we'll have a bit of an event and sit together and really enjoy it as a group."