Blades goalkeeper Steve Simonsen, the last player left on the pitch to try his luck, fired over the crossbar moments after opposite number Alex Smithies had scored his side's 11th kick as Town prevailed 8-7 after a goalless 120 minutes.
United have now lost all four of the play-off finals they have contested - and still not managed to find the net in any of them.
With three games to go this season they were second but, having lost top scorer Ched Evans to a jail term for rape, they were pipped to automatic promotion by rivals Sheffield Wednesday.
This outcome was particularly cruel on Simonsen, who had kept the Blades in the final with some fine stops as Huddersfield created the best of the game's few chances and then saved two of their first three spot-kicks.
Wilson said: "I can't think of a worse way to lose. Steve had a terrific game. Who would have thought it would come down to the two keepers? He feels doubly disappointed because of his performance. These boys are devastated, all their hard work has been taken away, it's very difficult to console them."