Sheffield United manager Chris Wilder praised the efforts of his men to see the match out for three points that keep them in sixth place.
“It was up to us to get about them. I thought we dominated and dictated the game in the first half,” said Wilder.
“Their goal was a disappointment for us, and all of a sudden it was game on. They have some good offensive players at the top of the pitch, so for us to see the game out was great.”
Norwich manager Daniel Farke felt his team had been “tired in the head”.
The Canaries took Premier League champions Chelsea all the way to extra-time and penalties in their FA Cup third-round replay at Stamford Bridge on Wednesday night.
However, on their return to league duty Norwich found themselves trailing after just six minutes when James Wilson, on his full Blades debut, put the visitors ahead following a corner.
United doubled their lead in the 68th minute when Clayton Donaldson capitalised on an under-hit pass back from midfielder Alex Tettey to score past goalkeeper Angus Gunn.
Norwich produced a swift reply and reduced the deficit within two minutes as captain Ivo Pinto headed in James Maddison’s cross.
Farke’s men could not conjure an equaliser though, as their four-match unbeaten Championship run came to an end.
“I’m pretty disappointed with the result,” said the German coach. “I think we were tired in the head, and we made some mistakes in our pressing and in our decision-making.”
Norwich City: Gunn, Hanley (Hoolahan 59), Zimmermann, Klose, Ivo Pinto, Reed (Vrancic 59), Tettey (Stiepermann 87), Lewis, Maddison, Oliveira, Murphy. Unused substitutes: Husband, Raggett, McGovern, Cantwell.
Sheffield United: Moore, Basham, Stearman, O’Connell, Baldock, Leonard, Lee Evans (Lundstram 82), Fleck, Stevens, Clarke, Wilson (Donaldson 58). Unused substitutes: Holmes, Sharp, Duffy, Lafferty, Eastwood.
Referee: T Harrington (Cleveland).