Wilder was unable to arrest the slide, as they ended the season having conceded 101 goals and accumulated just 16 points.
They started last season with a two-point deduction because of missed transfer payments in the 2022-23 campaign but challenged at the top of the division throughout.
A long-mooted takeover by American-based consortium COH Sports was completed in December, and Wilder signed a new three-year deal in January.
With seven games to go, they were two points clear at the top of the league. But they then lost three matches in eight days to Oxford United, Millwall and Plymouth Argyle.
While another defeat at Burnley - a fourth in five games - condemned them to the play-offs, despite finishing the regular season with 90 points.
They cruised into the play-off final with a thumping 6-0 aggregate win over Bristol City and took the lead in the final at Wembley against the Black Cats.
A second goal was controversially ruled out by VAR - the only match in the Championship in which the system was used all season - and Sunderland came back to equalise.
Then down to 10 men temporarily, with a player off injured and all their substitutes used, Tommy Watson score a 95th-minute winner for the Black Cats.
It stretched their wretched run in the play-offs to no successes from 10 attempts and leaves them facing up to another season in the second tier.