The Blades were held to a 2-2 draw at relegated Exeter on the final day of the campaign and fell behind when Alan Gow scored a stunning volley.
Wilson's side were then reduced to 10 men when James Beattie was red carded for a two-footed tackle on the Grecians' James Dunne. Goals either side of half-time by Lee Williamson and Kevin McDonald put them in front, but substitute Scot Bennett levelled for Exeter with the last kick of the game when he stooped to head home at the back post.
"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."