The Blades were trailing at half-time, Jay Spearing find the net for Wanderers.
And it proved to be the only goal of the game and left United empty-handed despite decent spells in the game.
Wilder said: “I’m obviously disappointed, we had the lion’s share of the play in the first half and should have been out of sight in the first 20-25 minutes.
“We started well, on the front foot, but a wondergoal changed the complexion of the game. Then we started the second half well and had enough of the ball in good areas, without showing the quality we have with the final pass.
“Bolton are an experienced team and had to defend deep, whereas we didn’t really have to do that. But ultimately, we’re very disappointed. We’re in a results business and we haven’t got one today.”