The victory, courtesy of a second half Anthony Pilkington header, was a third success in five league games, a run which has included four clean sheets.
When asked whether this was his finest hour as Norwich boss, Hughton replied: "It is, simply because it is Manchester United.
"They tested us more than anybody we have played against and were resilient enough.
"I suppose with the run we are on, the confidence we have from that we were able to show.
"It is certainly a wonderful achievement.
"It is a great feeling tonight because it is Manchester United, but it is still about three points.
"We had a few good performances at the start of the season where we did not get the points from our performances, so it was so vital we can pick up points.
"We have proved we can do, but we have to play our game at that level, because if we fall below that, then we can get beat.
"If we do that, it will give us a chance."