It means the Canaries have now lost five successive games on the road, which is hardly the ideal preparation for what looks set to be a season-defining four matches.
Sunderland head to Carrow Road next weekend before they take on Swansea, West Brom and Fulham - a run which Snodgrass is well aware could seal their fate.
"They are massive games," the Scotland international said
"It is a time for heroes
We need to try and do it against Sunderland.
"We got late goals at Southampton but it was not good enough from the first whistle to the last.
"We let ourselves down playing like that
We battled towards the end but we can't give a team like Southampton three goals
It doesn't work like that.
"I am bitterly disappointed and we will go on the training ground and try and put things right.
"We know what's good enough and we will look over the game, assess the situation and that will be a hard pill to swallow.
"Defeats like that ruin your weekend, ruins your week and by the end of the week you need to get it out of your head because we're in a dogfight."
Norwich's chances of beating the drop will rely heavily on their next four matches, given they then face Liverpool, Manchester United, Chelsea and Arsenal.
It is a miserable run-in and Snodgrass believes they will only be successful in staving off relegation if everyone at the club sticks together, which means rallying behind under-fire boss Hughton.
The odds on him 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.
"Everybody needs to stick together," Snodgrass said
"You're not going to get anything out of a relegation dogfight if you don't stick together so we need to do that as a team
"It is just not happening away from home right now
If you put performances like that in, it is definitely not going to happen.
"I really can't put my finger on it but we will keep going because we're in a relegation fight down there.
"We could go down so we just need to roll our sleeves up and keep going."
The only positive for Norwich was the manner in which they rallied late on as Johan Elmander and Snodgrass efforts reduced the deficit to one goal with five minutes remaining.
However, teenager Sam Gallagher's first Premier League goal eventually settled the nerves in stoppage time to ensure a 4-2 victory for the hosts - a result that left talisman Rickie Lambert relieved.
"It would have been very interesting in the dressing room if we had lost a three-goal lead," the England forward said.
"But we have won and that is all that matters
It was a good display apart from, obviously, the last five or 10 minutes."
Lambert started from the bench against Norwich but made an impressive impact when brought on early in the second half for Adam Lallana.
A minute after his introduction, the forward added to Morgan Schneiderlin's early strike and then showed impressive composure to provide the assist for Jay Rodriguez in front of on-watching England manager Roy Hodgson.
"I am always pleased to score a goal," he said
"I was determined to get on and do well for Southampton first and foremost and help the team get the points.
"Of course, I am still hoping to get to Brazil
It is my dream and everyone's dream so that is obviously at the back of my mind while I am trying to do well for Southampton as well."
Source : PA
Source: PA