Fulham looked to be heading towards another disappointing result when Adrian Mariappa gave the hosts an early lead, but four unanswered goals from the Cottagers, including one from Sidwell, saw them come back to claim a second consecutive win.
Pajtim Kasami scored a particularly memorable goal to level the scores, and Sidwell believes that such a strike was exactly what his side needed to kick-start their comeback.
"First of all it was a lot of hard work. Going a goal down too early was a bit of a blow but we knew if we kept plugging away, chances would come and we took them," Sidwell told Sky Sports News.
"We needed something special to get back into the game and [Kasami's strike] certainly was something special. Obviously we have all been under pressure, not just [manager Martin Jol]. Back-to-back wins put a lot of spirit in the camp and takes the pressure off."
Fulham now sit 14th in the Premier League table, while Crystal Palace remain 19th having lost their last five matches.