The Blades bossed the opening 45 minutes at home to Fulham, but went in at the break scoreless.
Let off the hook, Fulham took control of the game in the second half at Bramall Lane, missing an Aleksandar Mitrovic penalty but taking the lead through Ademola Lookman. It took a Billy Sharp penalty to ensure both sides recorded their first Premier League points of the season.
Adding to the Blades' frustration was the news that John Fleck will be out for four to six weeks with a back injury, whilst Max Lowe was concussed on his Premier League debut.
“It's mixed emotions,” admitted Wilder. “First half I thought we were in and around where we can be. I thought our control of the game was good, our shape in and out of possession was good. We created the better chances but we lost control of the second half and they came into it more.
“It was a game of two halves but to get a result with ten minutes to go and you're 1-0 down, we'll take that at the moment.
“In the first half we had the fluency I was looking for, but not second half. We lost control, made some poor decisions and looked a little bit anxious in our play. One mistake led to another and allowed Fulham back into the game. They took control and moved it about the pitch well and created the better chances.
“We rode our luck a little bit with them missing a penalty and missing a chance from Mitrovic late one.”
Sheffield United came into the game without a win this season and only two goals, one in the League Cup. Wilder says his players were low on self-belief in the second period.
“They looked a little bit anxious in the second half but they didn't in the first half,” he reflected.
“It's natural to see what's happening after a difficult start for us. That's what sport's all about. If it was that easy everybody would be at this level.”
Lowe's selection at left wing-back, which saw Enda Stevens line up in the back three, shows a manager looking for his best combinations at present. Wilder recalled Oliver Norwood and admitted he had considered changing both wing-backs. He also handed club record signing Rhian Brewster a debut from the bench.
“(Max) has got concussion and it's another desperately unfortunate situation for us following on from Flecky, Jack O'Connell and (Lys) Mousset (all injured),” said Wilder.
“There was a decision whether to start Jayden (Bogle) and Max, I made the decision just to put one in. It think it would have been too much of a gamble to stick both into a game we needed to get something from.
“He (Lowe) took a nasty whack and had blurred vision.
“I went with moving Enda to a position I didn't really want to move him to. Max coming off early scuppered all those plans.
“I talked to John (Fleck) after the Arsenal game and said he needed to get himself up to speed and I need him in the team. He'd gone up the road with Scotland and was pencilled in to play.
“He was unfortunate to land on such a small space on his back to do the damage he's done so it's going to be four to six weeks without John.”
Of Norwood, he said: “I don't think Ollie's hit the heights at the start of the season and I've got to pick the right team so he has to take a bit of responsibility for not being up to scratch but he's looked more like himself over the last couple of weeks.
“But I thought we lost a bit of midfield control in the second half. In the first half I thought Sander (Berge), Lunny (John Lundstram) and Ollie dictated that area of the pitch. I think Sander ran out of legs a little bit, the schedule he's had to deal with contributed to that, and John did a little bit too.”
Brewster came off the bench for the final 26 minutes, and it proved the toughest time of the match for his new team.
“That wouldn't have done him any harm at all,” said Wilder. “It was a big decision whether to start him but I thought he only had 50 minutes in him so I thought the best way to introduce him would be off the bench.
“It was a difficult 25 minutes for him. I think if we had flipped the two halves around and had control of the second half as we did the first it would have made it easier, he would have had more opportunities to show what he was about.”
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