The Cottagers are currently two points adrift of safety following back-to-back wins against Aston Villa and Norwich City.
Richardson now believes that he and his teammates have to get three points at White Hart Lane on Saturday to boost their chances of avoiding relegation.
"We have a big game on Saturday against Spurs and we need three points," he told Sky Sports News.
"We have had two wins on the bounce and can see some light. We have a big, big game on Saturday against Tottenham away and hopefully we will have a lot of away fans to come and support us and get behind the team. We are going to need them to get three points there.
"At this stage of the season we need three points - draws are not good enough - we need the win. It's exciting and a bit stressful but I'm excited and I enjoy a bit of pressure."
Fulham lost 2-1 to Spurs when the teams met at Craven Cottage back in December.