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The Blades have now picked up one point from their last three games after drawing against Birmingham and then losing back-to-back matches against QPR and Stoke.
Goals from Ben Wilmot, former Blade Phil Jagielka and Liam Delap late on sentenced United to defeat in Staffordshire, after Rhian Brewster scored his first goal of the season to drag his side back on level terms.
United's remarkable injury list forced them to line up with a back four in a rare change, something Neil had anticipated as a possibility after United played a similar shape amidst a fitness crisis earlier in the season away at West Brom in the EFL Cup.
And Neil said: "All the credit goes to the players. United normally play a back three but we prepared for them not doing that because of their injuries, they went 4-3-3 from the start and then went to a diamond.
"So for the players to be prepared for 3-5-2, 4-3-3 and a midfield diamond is a lot of work but you saw the understanding from the players and we carried it out really well. A lot of it's not on the grass work. It's mental work, giving an understanding of it.
"Can we find our spare players and hurt them? That's the easy bit. Painting a picture. Doing it on the pitch is the hard bit, as well as doing the basics. They did it all, so all credit to them.
"It's always going to be a tough game against Sheffield United. They've got a lot of players injured, as everyone knows, but so do we. Not just the lads missing but the lads coming back as well.
"We're only at the start of getting a few bodies back but if we can perform and have the same attitude as we did today, we'll be fine."
Despite the setback United remained top of the Championship table after second-placed Norwich City lost 3-2 at home to Preston North End. QPR have also climbed level with both United and City but sit third in the table on goal difference.
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