Max Dowman, 14, scored twice for the Gunners, along with Alex Marciniak.
Wilshere told arsenal.com: "I’m feeling good, and as I’ve said before, this group has a certain personality and fire. I also told them we’ve got to stop going two or three goals down, or I’ll be bald by Christmas!"
He continued, "I thought this was our best performance of the season. Birmingham are tough and strong, and it was a cup game they had to win, so we knew they'd come prepared. But we showed great character and personality, controlling the game and dominating the ball early on.
"We conceded two goals, which we need to review as part of their development is learning when to play, but overall, I’m very happy with the performance—some individual displays were brilliant."
On Dowman, Wilshere added, "Max’s performances speak for themselves, but there’s still a lot of room for development. For a 14-year-old, his character and personality are unreal. When we were 2-0 down, he was the one who wanted the ball, drove at their defence, and made things happen. His mentality to keep going, despite being kicked, and staying calm in those moments is impressive."