Canaries defender Max Aarons brought Cristiano Ronaldo down inside the area, and the United forward dispatched the resulting penalty past Tim Krul moments later.
It saw United move level on points with West Ham in fourth before the Hammers' trip to Burnley on Sunday, but goalkeeper David De Gea had to pull off a string of saves to keep them in the game.
Smith insisted if referee Darren England did not point to the spot, VAR would have let play continue.
"I am sure if the referee doesn't give the penalty to Ronaldo, they don't overrule it because it was as soft as can be," Smith said.
"Was their contact in the box? Yes. Is the arm on the shoulder? Yes. Is it enough to make the player go down? No.
"I could show you five or six other incidents like that in the game, so I am disappointed with that but in general I felt like Manchester United were able to dictate the game. Marcus Rashford gave himself a free-kick in the first half, so that was disappointing."
Ralf Rangnick admitted there were several areas where Manchester United could improve after the win.
"Norwich played in a very proactive and aggressive way, so it was a question of how do we deal with this kind of football," the German said.
"I wish we had more intensity up front, more physically and more willingness to win the one-v-one duels.
"We could have done better in some parts. In some parts it was good, like the whole defensive line, the six including De Gea were good.
"Offensively we also had some nice moves but didn't find the best solutions in the first half and second half after we scored goal, it is a question of intensity and we conceded too many free-kicks and corners.
"It was a game where something could never not happen and we need to change this."
De Gea was able to toast a second clean sheet in a row after fine saves to deny Teemu Pukki and Ozan Kabak in the second half.
Rangnick added: "It was a fantastic performance by David. He was probably man of the match, especially in the second half when he had two or three brilliant saves."
A worry for United was centre-back Victor Lindelof being forced off with what appeared to be breathing problems in the 74th minute.
But the interim boss provided a more positive update, explaining: "He can't even remember himself how it happened.
"I think he had a collision with another player and had problems to breathe. For more than 10 mins his heart rate was higher than normal and he was a little shocked by this, so we had to replace him.
"The doctor has checked him after the match and it seems everything is okay now, but we still have to see how he is doing tomorrow. Hopefully he will fit for the Brentford game."