Rene Meulensteen's men sit 17th in the Premier League and missed out on an opportunity to pull away from the relegation zone on Tuesday when they were beaten 2-0 at Swansea City.
With matches against Manchester United and Liverpool on the horizon, Richardson feels it is imperative Fulham take maximum points from visiting Southampton this weekend.
"We can’t dwell on Swansea as we’ve got a big home game coming up which is a must-win for us," said the former England international.
"We've got to focus on Southampton now. It's a massive game and we're going to need great home support on Saturday.
"We know we've got to roll our sleeves up and put a big performance in because we owe the fans that.
"Like I said, it's a must-win three points for us."
Fulham were beaten 2-0 in the reverse fixture at St Mary's Stadium in October.
