The Eagles fought well away to the Premier League leaders – who were seeking a seventh consecutive win in all competitions – but were undone by a familiar face, Ebere Eze, shortly before the break.
Palace continued to battle and threatened the Arsenal goal with a series of late attacks, but ultimately were condemned to defeat.
But Richards and his teammates saw positives in the display, with the defender reflecting: “We played really well against the top team in the league, one of the best teams in Europe.
“Us being disappointed with the result today just shows how far we've come. We've done a lot in the last year, and we have really high standards for ourselves.
“I think we all came into the changing room feeling like we left a little bit out there, and again, that shows how well we've been doing and how optimistic we are for the future.
“We restricted the best team in Europe to only one or two clear-cut chances. I think at the Emirates, it's always a tough game to play, but especially with the form they're in right now.
“We created a lot, we defended a lot, and we got unlucky with their goal – but regardless, there's a lot to build on today.”