Donny's 1-0 defeat at the King Power Stadium against Leicester City, combined with Birmingham City's late comeback in their 2-2 draw against Bolton Wanderers, has condemned Paul Dickov's side to League One football next season.
Nugent came close once more to finding an opener when played through by Danny Drinkwater, only for Sam Johnstone to deny the striker his 20th league goal of the campaign when he pulled off a fine save.
The hosts continued to push and Riyad Mahrez's towering header almost undid Doncaster, yet the ball whistled just over the crossbar.
Nugent forced Johnstone into another save from a tight angle shortly after the hour mark, while Mahrez also saw his strike well handled by the keeper.
Leicester did eventually break the deadlock, however, when James Husband tripped Mahrez inside the box. Nugent stepped up to take the resulting penalty and made no mistake firing the ball into the top corner.
Billy Sharp came off the bench for Doncaster and nearly levelled the contest late on, but he was unable to find the target when meeting a free kick at the far post.