Robert Snodgrass scored the only goal of the game at Carrow Road to hand Norwich just their second win in 14 matches, edging them four points clear of the Premier League relegation zone in the process.
"This season, this would be our best performance I think. We were very good at Stoke away, we were very good at Chelsea, and Man United for 45 minutes was arguably our best. We all accept we're getting into the part of the season when the pressure's on," Hughton is quoted as saying by PA.
"We've certainly been very good for the last three games. That's a wonderful standard to see. We just need to alleviate a little bit of this pressure on ourselves, by perhaps getting the goals that can do that. What gives me confidence is we have a really good group of players who work hard, and the training ground is a good place to be.
"They feel it and they are as frustrated as anybody. It's a good place to be, certainly when you're getting good results. This performance underlines that they care, and they are desperate to make sure they are Premier League players next season. First and foremost they will work hard each day, that's their responsibility, they want to do well and they want to stay in the team. That has to be their drive."
The Canaries face an important spell in the coming weeks, with matches against Aston Villa, Stoke City, Sunderland, Swansea City, West Bromwich Albion and Fulham over March and April.