Andy Morrell starred as Blackpool ended Swansea's play-off hopes, but Bristol City's win over Rotherham meant the Seasiders missed automatic promotion.
Morrell's striking prowess was too much for the Swans
Izzy Iriekpen's header gave Swansea the lead, but Morrell equalised after a good run and Keigan Parker made it 2-1.
A fine swivel and shot from Lee Trundle made it level and, after Trundle blew a penalty, Iriekpen put the Swans ahead.
But Morrell struck three more in quick succession and Parker rounded off the scoring a minute before full time.
The defeat was Swansea's second in 12 games under Roberto Martinez.
Slim consolation for the sold-out Liberty Stadium crowd will be that Oldham's 1-0 win over Chesterfield meant Swansea would have needed to have won by four clear goals to have made the play-offs.
Blackpool will carry fine form into the knockout stages, having won seven straight games and lost just once in the last 14 matches.
Swansea: Gueret, Amankwaah (Abbott 67), Austin, Iriekpen, Lawrence, O'Leary (Williams 46), Britton, Robinson (Allen 75), Craney, Trundle, Darryl Duffy.
Subs Not Used: Oakes, Richard Duffy.
Goals: Iriekpen 14, Trundle 47, Iriekpen 55.
Blackpool: Hart, Jackson, Williams, Barker, Evatt, Southern, Forbes (Fox 77), Jorgensen, Hoolahan (Gillett 84), Parker, Morrell (Vernon 84).
Subs Not Used: Coid, Gorkss.
Goals: Morrell 25, Parker 32, Morrell 57, 61, 78, Parker 89.
Ref: A Marriner (W Midlands).