Manager Felix Magath celebrated his first away win since taking charge of the London club as goals from Richardson and Hugo Rodallega helped them to three vital points.
The Cottagers now remain five points adrift of safety with five games remaining after West Brom and Crystal Palace also won, but Richardson believes the victory will give them impetus for their survival push.
"It was a massive win for us today," he told Sky Sports. "You saw the way the players and the fans celebrated - we needed the win and we got it.
"We've won two games out of our last three, we've got good form and now we're at home (against Norwich next weekend) so hopefully the fans will get behind us and we can beat Norwich.
"We're down there - we need to get out of it and I'm more than confident we can do it."
Meanwhile, half-time substitute Rodallega was pleased to score the winning goal with four minutes to go.
"I'm happy because the team worked hard," said the Colombian.
"The last two results have not been good for the team so now everybody is happy in the dressing room because these three points are very important for us.
"Everybody is working hard for themselves, the manager and the club."
Felix Magath felt the Londoners needed five wins to avoid the drop before Saturday's win at Villa and Rodallega believes they can now go on and achieve the rest.
"Yes, I believe so," he added. "The team is ready, but we're just happy for today."