Keith Curle's men put up a spirited fight at Pride Park, but the Sky Bet Championship side proved to be too good on the night and deservedly progressed.
It is the Rams who now get the chance to entertain Manchester United in the last 16, while the Cobblers can turn their attention to securing promotion from league two.
But although Town were beaten on the pitch, they were the winners off it as they were cheered on by an amazing travelling army of close to 4,500 supporters.
It was an amazing turnout for a league two side to take to an away game on a midweek night, and despite the result they enjoyed their evening.
Their support was rewarded with those two second half goals for Nicky Adams and Sam Hoskins, and the majority of the fans stayed on until the end to salute Curle and his players for what has been an exciting FA Cup run, and the club's best since 2004.
Photographer Pete Norton was at Pride Park to capture these images of the Cobblers fans in the away end..
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Town got themselves into the hat for fifth round draw for the first time since 1970 | Getty Photo: Pete Norton
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The majority of the 4,442 Cobblers supporters stayed to the end to cheer their team off | Getty Photo: Pete Norton
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The Cobblers can now turn their attention to winning promotion from Sky Bet League Two | Getty Photo: Pete Norton
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Town scored their second half goals through Nicky Adams and Sam Hoskins, who netted a late penalty | Getty Photo: Pete Norton