Palace were beaten 1-0 via a goal from former Eagles star Ebere Eze.
Richards told Palace's website: “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.”
On Eze's acrobatic winner, Richards wryly stated: "Definitely seen it on the training pitch a lot and also on the field, but when he was wearing our colours. I wish he hadn't have scored today, of course, but happy for him regardless.”