Tuesday's 3-1 home defeat to Everton was Villa's 18th loss from 28 league games this season, leaving them eight points adrift of safety with 10 fixtures remaining.
Villa have won just three top-flight matches in 2015-16, but skipper Richards still believes they can still pull off a great escape.
"It's more tough games coming up - Man City and Spurs - it's not getting any easier," Richards told the club's official website.
"But we will keep going. We are not giving up. We will keep believing.
"I know it's hard for everyone associated with the club, especially the fans.
"I feel their pain because Aston Villa - in this situation - it's hard to take. That goes for the players too obviously. It's hurting us all.
"When people say that it doesn't hurt us, as players, that hurts the most because we don't want to go out and lose every week. It's not good.
"All we can do is go out there and do our best."