The Canaries - who still need a couple of wins to secure top-flight status - produced a resolute battling display and took the lead after 56 minutes through Michael Turner's close-range header.
With the clock ticking, Arsenal were handed a way back into the match with just five minutes left when the assistant referee spotted a shirt pull on Olivier Giroud by Kei Kamara.
Mikel Arteta kept his cool from the spot to level before Giroud's close-range effort turned the match around and substitute Lukas Podolski wrapped things up in stoppage time.
Hughton said: "My first thought is that it was not a corner in the first place but what I am more aggrieved about is there is contact with Kei, but he swivels and plays the ball.
"You have a linesman who makes a decision from 40 or 50 yards away and the referee who is eight yards away and has the perfect view. Their third goal was also offside.
"I have had a private conversation with the referee but I am still not convinced."
Hughton must now regroup his squad for the visit of Reading and games with Stoke and Aston Villa, which will ultimately define the end to their campaign.
"Our season was not going to be about what happened here or at Old Trafford," said the Norwich boss. "We have five games now, three at home, so we need to get enough points to keep us where we want to be.
"Generally we have been good at home, so there are opportunities for us, but we have to take those."