The league champions, Sheffield, finished 18 points ahead of London Towers in the table, but lost 85-78 to the fourth-placed team in Saturday's semi- final.
The runners up, Manchester, finished the regular season 12 points clear of third-placed Thames Valley, but went out 79-76 to the Tigers in the second semi-final.
This time Sheffield and Manchester lost only the chance to crown their successful season with the domestic game's most glamourous but least meaningful title. But next season, when the League is arranged into conferences, the title of League champions will go only to the team that gets it "right on the night" in the play-off final.
In the play-off for third place, a game neither team envisaged playing in, Sheffield raised the intensity level by recovering from 10 points down at the end of the first quarter to lead 47-43 at the interval.
The Sharks held the edge in a tight third quarter then took control with a 17-0 fourth quarter run, including 10 points from Todd Cauthorn, to win 98-88.
Tigers, beaten by Birmingham Bullets in last season's play-off final, survived a devastating injury to playmaker Casey Arena against Manchester on Saturday. He damaged knee ligaments colliding with former team-mate Tony Holley with two and a half minutes left in the first half and was ruled out of last night's final.
Holley later lost the chance to save the game for Giants when he missed three free throws on the buzzer, costing Manchester a second title to add to the League Trophy they won in March.
Sheffield were bidding to become the first League winners since 1993 and to also take the play-off title and complete a treble after winning the National Cup in January. But a 49-45 halftime lead, when Randy Duck made the most of Tower's home-court advantage with six-successive points for a 57-55 lead.
Duck led London's scorers with 21, supported with 19 from Malcolm Leak and 18 from Martin Henlen, who revelled in the play-off atmosphere after two seasons in Greece.
Terrell Myers, whose last-second shots won both the Cup and League titles for Sheffield, led their scorers with 28 points. But poor shooting in the final quarter from Sheffield allowed Towers to take a match-winning 84-74 lead with 40 seconds to play.
Even so, Sharks are determined to re-sign their leading players for next season. Their general manager, Yuri Matischen, said: "We've opened negotiations to get all our key players back." The club have already agreed terms with their coach, Chris Finch.
LEADING SCORERS (play-off semi-finals): Tigers: Siemon 19, Walker 11, Balser 11, McCord 21. Giants: Dorsey 28, White 22, Holley 13. Sharks: Myers 28, Payne 20, Johnson 15. Towers: Duck 21, Leak 19, Henlan 19, Morton 14. (Third-place play-off): Sharks: Conlan 27, Myers 20, Cauthorn 19, McKinney 13. Giants: Dorsey 29, White 26, Holley 12.Reuse content