The Devils managed just one heat win all night and that came in the 11th through Jack Holder, who top scored with eight points.
Rye House were totally dominant with Robin Aspgren and Anders Mellgreen both claiming paid maximums.
The Devils have to pick themselves for another cup meet at Peterborough on Sunday.
Rye House 66: Ed Kennett 10, Robin Aspgren 13+2, Anders Mellgren 13+2, Steve Boxall 9+1, Nikolai Jakobsen 9+2, James Sarieant (G) 6+2, Jan Graversen (G) 6
Devils 24: Ryan Fisher 1, Jack Holder 8, Sam Simota 5+1, Kyle Newman 4, Morten Risager 5, Matt Williamson (G) 1, Ashley Morris 0