The Blades have returned to the top of the Championship table with their victory in Staffordshire, but the triumph was overshadowed after Coutts suffered what appeared to be a broken leg just before half time.
Wilder has acknowledged that returning to first place in the standings is an "outstanding achievement", but preferred to focus his attention on Coutts, who has been an ever-present in his starting lineup this season.
The 50-year-old is quoted by BBC Sport as saying: "Getting a result that takes us back to the top of the Championship is an outstanding achievement. A lot better teams have been turned over here in the last 15 or 16 months so we knew this wasn't going to be an easy place to come and with Nigel's connections to the club it always adds an extra little bit to it.
"We are a fair team and a committed team and unfortunately through the course of games, seasons, careers you pick up these injuries and we have picked up a nasty one.
"We are a bit subdued. It's a difficult situation because we were outstanding and deservedly won the game."
Wolverhampton Wanderers will return to top spot if they can avoid defeat at Reading on Saturday afternoon.