The Cottagers saw their 13-year stay in the top flight come to an end last term as they finished four points adrift of safety.
Despite admitting that the 2013-14 campaign was a hugely disappointing one, Heitinga hopes that the club can bounce back as soon as possible.
"It's a feeling that is not nice," the Dutchman told Fulham's official website. "I've been here for more than three months, played 14 games, and unfortunately we didn't have enough to survive in the league.
"It's more that we disappointed people inside and outside the club; the chairman, the fans. They don't deserve this and hopefully we can manage to come back in one season."
Heitinga joined Fulham from Everton during the January transfer window.