Andy Reid fired United ahead in the 17th minute with a fantastic 25-yard free-kick but defender Michael Nelson headed Norwich level within three minutes.
Richard Cresswell put United back in front after 29 minutes although Norwich replied for a second time in the 64th minute when Wes Hoolahan converted from the penalty spot.
Hoolahan then grabbed the winner with six minutes left with his second spot-kick conversion after Kyle Bartley was penalised by referee Phil Crossley for handball.
The Blades then finished the game with 10 men when Stephen Quinn was sent off for violent conduct after a bad foul on Hoolahan, who duly claimed the match ball in injury-time.
Carver, whose side have now lost on their last five visits to Carrow Road, said: "It's not just one decision I'm upset about there were at least six of them. They are the sort of decisions that can cost people their jobs and send home supporters who have travelled more than four hours to get here home unhappy.
"I had my say on the pitch in a controlled manner and then waited the 30 minutes before sitting down and discussing the incidents with the referee. I think one or two things will come out in the next few days."
Source: PA
Source: PA