Wilder claimed goalkeeper Joe Lumley should have kept out Keane Lewis-Potter’s curling effort 16 minutes from time which condemned Boro to a second home loss in four days.
The hosts tried to hit back, Aaron Connolly missing the target and Hull goalkeeper Matt Ingram turning over Marcus Tavernier’s long-range drive, but Hull held on to leave their opponents in eighth place, three points shy of sixth-placed Sheffield United with a game in hand.
Chris Wilder, whose side travel to second-placed Bournemouth on Good Friday, said: “This is the business end of the season, we have missed an opportunity. That is the disappointing aspect of it.
“But there are quite a few teams who would swap positions with us. We want to keep going and adding to the points tally.
“I am disappointed. That’s what happens if you’re not at it and your standards aren’t very good.
“For 20 minutes we were OK, but it deteriorated in to a poor performance individually. We gave the ball away too cheaply. There were individual errors and you could see that result coming.
“It was that kind of performance. That is one of our poorest performances of the season at home.
“The goalkeeper should have done better. I have protected him for long enough and it was another poor goal. He should have done better.
“It wasn’t going to be a walkover. They have really good young players. They aren’t just seeing the season out and their reaction at the end is not a reaction from a team seeing the season out.”
Boro, who lost at home for the second time inside a week, failed to make the most of an opportunity to climb into the Championship’s top six as Lewis-Potter settled the contest with 16 minutes remaining.
It was a blow for the home side in the wake of Sheffield United’s goalless draw with Bournemouth earlier in the day, the defeat dropping Boro to eighth, three points shy of the sixth-placed Blades with a game in hand.