On an afternoon when Premier League referee Anthony Taylor sent off a man for each side and gave a number of head-scratching decisions, Billy Sharp’s double and a late goal from David McGoldrick sent Chris Wilder’s men to within four points of second place in the Championship.
The first half was a closely contested affair as both sides hit the woodwork but the Blades took advantage within two minutes of Smallwood's dismissal.
And Mowbray said: “It was an Intense football match, two teams who were at it. Sadly I would say the officials had the biggest impact on the game today.
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“I think the referee mismanaged the game. He's come from the Premier League to the Championship, thought he'd have a nice easy day and he's guessed his way through the match with his decisions.
"He's upset the stadium, upset our bench and I think he had the biggest impact on the game.
"The last 20 minutes we need to be better. The sending off of Smallwood...I think psychologically and mentally we have to deal with that better from being in total control when it was 11 v 10 to 10 v 10 - they dealt with it better than we did.
"We were pretty good. I think when you come to Bramall Lane, if you don't stick the armour on and get the sword out, you're going to get beaten.
"They're a really good football team, with a really good manager."