Hughton's men fell 2-0 behind after less than an hour as Morgan Schneiderlin and Rickie Lambert put Southampton in command.
The 55-year-old responded by bringing on Ricky van Wolfswinkel, Nathan Redmond and Johan Elmander in a triple substitution that attracted the ire of the travelling supporters at St Mary's Stadium.
Jay Rodriguez then put Southampton three to the good before Elmander and Snodgrass scored late on to give Norwich hope of a dramatic comeback.
But Sam Gallagher netted in injury time to seal victory for Southampton and Hughton admitted he has sympathy for Norwich supporters.
"It's never nice (being criticised), but I understand," Hughton said.
"We had more than 2,000 supporters travel down and it's their club and their team and they want to see a Norwich team which is really competing and allowing themselves to be really competitive in the game.
"What they saw for longer periods was a Southampton team that is better than us.
"It's not nice, but as manager you have to take all criticism on the chin and look for a response in the next game."
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