Sidwell said that the performance against Everton in the 3-1 defeat was encouraging, and believes that the supporters can spur the players on to victory away to Aston Villa on Saturday.
"You've just got to dust yourself down and get on with it as quick as you can," he told the club's official website. "Obviously we've got six cup finals now and we need to start picking up points so we can't dwell on the fact that we've put in a good performance [against Everton].
"Mathematically we've still got the time to get ourselves out of trouble, but we need to start winning the games now because before you know it six games becomes four and then it starts to look not doable. It comes down to Saturday's game and won that we need to win.
"The fans have been brilliant, absolutely fantastic. I believe we've got a few travelling up to Villa Park at the weekend and it makes a big difference, especially away from home."
Fulham, currently bottom, are five points clear of safety in the Premier League.