The Hawks missed out on a play-off spot as they were held to a 0-0 draw by Tonbridge Angels at Westleigh Park.
Dover’s dramatic stoppage-time win ensured they will instead by in the hunt for a place in the Skrill Premier for next season.
It was agonising for Hawks who missed a penalty through Scott Donnelly in the first half.
Meanwhile. Gosport Borough lost their final match 2-1 at home to Bromley.
Sam Pearce scored for Borough but they could not rescue a point and saw their season end with defeat.
In the Wessex League premier division Horndean crashed to a 5-0 loss at home to Sholing.
Bognor were beaten 4-2 at East Thurrock in the Ryman League premier division.
It means the Rocks finished third in the table.
They will be in play-off action on Wednesday at Nyewood Lane.