Felix Magath's men claimed a 2-1 win at Aston Villa last weekend to move off the bottom of the Premier League and a victory over Norwich on Saturday would cut the gap to safety down to just two points.
City, who sacked manager Chris Hughton following a 1-0 loss to West Brom, face Liverpool, Manchester United, Chelsea and Arsenal in the run-in, meaning Fulham can put them under huge pressure as the relegation battle reaches its climax.
And Stockdale, who has started the last four games ahead of Maarten Stekelenburg, insists that Fulham have everything they need to avoid the drop.
"There's some fight in that dressing room and we've believed all along," Stockdale told Get West London. "When things fall into place we might win these games comfortably but for now we've just got to keep playing.
"The character is there. The players are there. The ability is there. We all know that, but we just need things to click into place for us.
"There's five more games now and we're still five points adrift so we carry on. Nothing has changed really because we've won at Villa.
"We're still five points adrift and we need to catch Norwich."
