Despite staging an improbable late comeback at St Mary's, the Canaries were unable to avoid falling to a 4-2 defeat - their fifth in succession on the road.
Given they face Liverpool, Manchester United, Chelsea and Arsenal in the final four fixtures, matches like the one at Southampton are the kind of games Norwich need to win if they are to beat the drop.
The odds on Hughton leaving Carrow Road shortened after the loss on the south coast, where the Norwich boss was subjected to chants of "you don't know what you're doing" after making a triple second-half substitution.
"For the majority of the game a very good Southampton team were better than us and if you concede three goals like we did you make life very difficult for themselves," Hughton said.
"It's never nice to hear those chants but I understand. We have more than 2,000 supporters who have travelled to watch the game and it's their club and team, and they want to see a team competing.
"What they saw for too long a periods was a Southampton team that were better than us. It's never nice but you have to take the criticism on the chin."
Southampton had a three-goal lead heading into the final five minutes courtesy of efforts from Morgan Schneiderlin, Rickie Lambert and Jay Rodriguez, only for sloppy play to allow Johan Elmander and Robert Snodgrass to net.
However, Norwich were unable to eke out a draw and teenager Sam Gallagher put the game out of sight in stoppage time.
"The two goals certainly flattered us," Hughton said. "If the game had finished 3-2, it wasn't a 3-2 game. They were far better than us today.
"But we did get the two late goals so if I am looking for any pluses then we have showed enough character in that final period to get back into the game, irrespective whether we deserved it or not.
"We know it's tough because we have been very inconsistent but we are capable of doing it."
Norwich sit four points off the relegation zone with eight matches remaining, while the win saw Saints usurp Newcastle in eighth.
Victory was a fine end to a week which saw Ralph Krueger appointed chairman, but manager Mauricio Pochettino was frustrated at the end by Saints' slack defending at the end.
"It's a great lesson that we have to learn from today's game," the former Argentina defender said.
"We're a young side that's still growing and the main lesson today is that, obviously, the game is not finished until the final whistle has blown.
"I thought the game was overall controlled. It is true that when Rickie Lambert came on his contribution was very good and was great for the team and also Sam Gallagher's contribution was very good.
"It is true that we're well satisfied with the game at 3-0, but it goes to show that when you lose a little bit of focus, you lay your guard down, we basically made two quick mistakes, we conceded two soft goals and, again, it is a lesson we have to learn."
It was not all bad at the end, though, as 18-year-old Gallagher managed to net his first Premier League goal to secure victory.
"We all know what Sam has been going through," Pochettino said, referring to the recent passing of the striker's father.
"He has been going through a really tough time. It doesn't change his situation, but it will go a long way to making him happy and his surroundings and his family - everyone around him that wishes the best for him. It will be a good thing for him."