Exeter will mark their centenary year in the
Nationwide Conference after suffering relegation from the Football League on the final day of the season.
Victory over Southend was not enough to keep Gary Peters' side up, with Swansea securing the win they needed.
The match kicked off 15 minutes late and the result from Swansea meant Exeter already knew their fate long before the final whistle.
They were already down when Steve Flack slid in a last-minute winner, following a series of chances for the home side.
Exeter had looked in deep trouble when they conceded a penalty in the sixth minute,
but goalkeeper Kevin Miller saved Tes Bramble's spot-kick.
But from that point the home side were the better team and deserved their late winner.
For joint chairman John Russell, it was his second relegation from the league in four years, after his Scarborough side dropped out in 1999.
Exeter: Miller, Hiley, Gaia, Baker, Todd, Coppinger, Pettefer,
Ampadu, Walker, Flack, Devine. Subs: Fraser, Roscoe, Kilheeney,
Southend: Flahavan, Beard, Searle, McSweeney, Cort, Darby,
Jenkins, Strachan, Maher, Rawle, Bramble. Subs: Gay, Thurgood,
Henry, Salter, Kightly.
Referee: M Fletcher (Worcestershire)