Fulham have been bottom of the table for the past seven matches but narrowed the gap to safety to just four points after a 1-0 win over Newcastle United on Saturday.
Ashkan Dejagah struck the only goal of the game at Craven Cottage to record Fulham's first win since New Year's Day, and their first under Felix Magath.
Stockdale, who was recalled in place of Maarten Stekelenburg in goal, revealed they had been inspired by pictures of supporters stuck on the dressing room wall by Magath.
"The manager didn't need to say too much to us before the game - we had pictures of fans on the dressing room walls, and a few other bits and pieces, to remind us what we're fighting for," Stockdale said.
"I took a good look around because it was a reminder of the good times we've had in the six years I've been here, and a few of us who have been at the club a while - Brede Hangeland, me, Steve Sidwell - agreed, 'This is what we've got, this is who we're playing for.'
"You don't walk into a changing room every day and see pictures of fans staring down, but they all wear the badge with pride and we know how much Fulham means to them.
"The manager deserves credit for the pictures, and putting us through new things and schedules.
"As a certain midfielder at the club told me last week, it's not just the badge on the front of the shirt we're playing for at the moment - it's the badge on the arm which says 'Premier League'. That's when it really hit home to me how important it is for us to stay up."
Fulham face a daunting trip to Manchester City next weekend, but have crucial matches against fellow strugglers Norwich City and Crystal Palace in their run-in.
