A Latics side including NINE Academy products gave as good as they got against the Londoners.
And substitute Divin Baningime kept a cool head seven minutes from time to cut inside the last Arsenal defender, before slotting home the only goal.
"I'm made up for all the lads," said Richardson. "We've been quite consistent with our team selection in this competition, and we've also been quite consistent with the performances.
"I thought the lads worked tirelessly hard in and out of possession and, when the chance came, Divin took his chance very well.
"For a young lad to score the winning goal in a cup quarter-final, those memories don't come along every day.
"I thought the turn-out was excellent, they got right behind the lads, and they were treated to a very good game.
"It was a lot of our young lads against a team of elite young players in the country, and our lads went toe to toe with them and showed how good they are.
"I thought Chris Sze led the line superbly, obviously Thelo Aasgaard's a talent in himself, to the lads at the back, James Carragher and Charlie Hughes, Harry McHugh in midfield.
"We expected them to see a lot of the ball, but we stuck at the task and, on the balance of play, it was quite even.
"It was always going to be won by an individual bit of brilliance, and fortunately it was one of our lads that provided it."
Also through to the last four are Hartlepool, Rotherham and Sutton.
The draw for the semi-finals is on Saturday night.