The Blades drew 2-2 on the final day of the season at Exeter City with goals from midfielders Lee Williamson and Kevin McDonald; a win could have handed United promotion had rivals Sheffield Wednesday failed to beat Wycombe Wanderers.
United came from behind at St James Park, but only after being reduced to ten men - James Beattie sent-off for a dangerous challenge.
"We went hammer and tongs to try and get second place and congratulations to Wednesday, they have got there," said Wilson. "They have shown great consistency in the last two months, but from our point of view we have had a couple of setbacks.
"But we are very positive about going into the play-offs. We wanted to go up and we didn't get there, we came up slightly short. There was a cigarette paper between automatic and not.
"Stevenage is a very tough tie and we take nothing for granted. Our preparations will be thorough. We have got two very difficult games in front of us but we are confident."