Stockdale struggled to contain his emotions after Fulham's fate was sealed, courtesy of an emphatic 4-1 defeat to Stoke City at the Britannia Stadium.
Fulham's 13-year stay in the Premier League will come to an end after next weekend's home game against Crystal Palace.
And Stockdale believes he and his team-mates must finish with a flourish, even though they can no longer escape the bottom three.
"We have to do it for the fans. We have to get three points for the fans, because that's all they deserve - nothing less," Stockdale told Fulham's official website.
Reflecting on a miserable afternoon for Felix Magath's men at Stoke, the goalkeeper expressed gratitude for the support Fulham received from their fans.
"What can I say? They're the best thing about today," he added.
"They stayed until the end, they clapped, they stayed until after the whistle. They stayed with us through the lows and I think they deserve better than that.
"It's hard to stand here and put anything into words really.
"I've gone through it (relegation) before on loan (with Plymouth Argyle), but never for one of the clubs that I love, which is Fulham.
"They gave me a chance, and it's just disappointing you can't give it back to keep them where they belong."
Asked if he had a message for Fulham's fans, Stockdale said: "Stick with us. We're trying to bounce back next year.
"There are a lot of players who believe in the club and want the club to be back where it belongs."
