After two solid seasons back in the Premier League and a summer of spending, the Canaries' start to the campaign has fallen short of expectations.
An opening day draw with Everton at Carrow Road was last weekend followed by a 1-0 defeat at newly-promoted Hull, who were down to 10 men for the most part.
It is a disappointment that Norwich have responded well to and, having beaten Bury 6-3 in the Capital One Cup second round in midweek, they today overcame the Saints thanks to Redmond's second-half solo effort.
"It is a better day than last Saturday," Hughton said. "That's what the game is about.
"There was nobody more disappointed with the result last week, and perhaps the performance, than myself and the players.
"That being the case, you want to do something about it.
"It has been a good week and we got a lift off Tuesday night's game, winning and scoring some goals, and we were able to take that feeling a little bit into today.
"It was always going to be a tough game. Southampton are a very good side and they have invested very well on top of an already talented squad of players.
"I think in the end it is a good result for us, but I think over 90 minutes we deserved it.
"I think we shaded it. They had to go for it in the last bit of the game and it became very open, but they are a good side and I think they will have a good side."
The difference today was teenager Redmond, who proved a handful throughout.
The 19-year-old summer signing's pace often had Southampton on the back foot and saw him score the decisive goal in the 68th minute, cutting in from the left to unleash a fierce drive from the edge of the box.
"He is an exciting young talent," Hughton, who also managed Redmond at former club Birmingham, said.
"I always understand when somebody is in really good form, particularly if they're a young player, there will be interest in them.
"I think that is normal, but we have all been around long enough to know that also with young players they can have highs and lows and you have to be sure to look after them in the right way."