The Irons, who last won against Chelsea on December 1, went ahead through a Mark Noble penalty after just three minutes when referee Mark Clattenburg spotted a shirt pull by defender Ryan Bennett on Winston Reid.
"The key decisions in the game did not go in our favour, but we did not start well enough," said Hughton, who confronted Clattenburg as he left the pitch at both half-time and following the full-time whistle.
He added: "We accept Ryan Bennett had hold of the lad's shirt, but I also saw Reid's forearm in Ryan's chest. They are very close, he is not pulling Reid so he cannot get away, it is something you see game in and game out right throughout the country."
Norwich midfielder Robert Snodgrass rattled the woodwork with a free-kick before Joey O'Brien crashed home a second goal after 26 minutes, which proved enough for a morale-boosting victory ahead of next weekend's FA Cup tie against Manchester United.
Russell Martin netted a late consolation with a well-taken volley for his third goal in two games.
"On almost every occasion you do not see a penalty, particularly when it is so early in the game, so I was very surprised when he gave it," Hughton said. "I also don't accept it was not a foul on Alex Tettey leading up to the second goal and certainly was a handball in the first half and then the incident on Harry Kane."
The Hammers, meanwhile, got their campaign back on track following a run of just two victories in the previous 11 outings. Carlton Cole had missed a great chance to make it 3-0 when he blazed over from close range before the break, while Ricardo Vaz Te also saw his second-half header come back off the post.
West Ham manager Sam Allardyce feels his side are moving in the right direction. "I was wondering if we were going to hold our confidence and performance level at home," said Allardyce, who felt the referee had a "great view" of the penalty and made the "correct decision."
"It has been really good even though we have had two back-to-back defeats but today they showed they have the mentality to cope with whatever is thrown at them."
- Sports & Recreation
- Mark Clattenburg