Gary Ablett's men currently lie 21st in League One and have been in administration since April.
And Raynes told the club's official website: "We need a win just to pick the place up a bit.
"I think a nice cup run would take away the pressure of the league. Tooting seem a decent side and they are going to be no mugs, but we know we can beat them and hopefully we'll have too much for them."
When asked about the financial benefits of the competition, Raynes added: "If we had beaten Gillingham last year, we would have got the £100,000 or so from playing Aston Villa which could have saved the club from going into administration. So we know the money that can be made out of the FA Cup and how important it could be for the club."