The Rams failed to overcome a 21-point deduction for falling into administration.
"We've been relegated, but I've never seen a team get relegated and [get] the reaction of the fans," Rooney told Sky Sports after the final whistle. "I thought it was incredible, the support the fans gave the lads all season. Of course, [I'm] disappointed, sad, upset - but [I'm] proud."
"In some ways, we can draw a line under what's happened and really start the rebirth of this club and try to move forward.
"I want to rebuild the club. You see what it means to the fans every week, this is a special club, a big club and we're all proud to be here. I want to be the one to bring the happy days back."
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