Back-to-back wins over Aston Villa and Norwich City have seen Fulham climb to within two points of safety with four matches left to play.
And Richardson senses a new confidence among the squad that they will still be plying their trade in the top flight next season.
"We've had two wins on the bounce and we've seen a bit of light," he told Sky Sports. "We've got a big game on Saturday against Spurs and we need three points.
"At this stage of season, we need three points. A draw is not good enough.
"It's exciting. A bit stressful, but I'm excited.
"We try to take one game at a time. We want to win all our remaining games.
"Everyone is fighting for survival and we want to do it as well."
Richardson was part of the West Brom team that survived on the final day of the 2004-05 campaign, but is hopeful it does not come to that this time around.
"I hope it doesn't go down to the last day," he added. "If it does, the lads will be a bit itchy.
"Hopefully we can wrap it up before then."
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