Hughton has come under pressure with his side languishing in the Premier League relegation zone, boasting just eight points from 10 games.
Norwich's last two fixtures have brought heavy defeats, Saturday's 7-0 drubbing at Manchester City coming on the back of a 4-0 League Cup loss against Manchester United.
Yet Martin feels the players must take responsibility for turning things around.
"We're all behind the gaffer. That still remains the same," the defender told BBC Radio Norfolk.
"We've not been good enough. He'll get a lot of stick for that and so will we.
"It's up to us to take some responsibility and accountability for what's gone wrong.
"I'm sure we're going to take (criticism) all week until the next game."
Martin has no issue with the condemnation that has come Norwich's way following their weekend defeat.
"When we win we deserve the praise and by the same token after that we deserve what we get from the media, fans and ultimately ourselves. We are embarrassed and hurt," he added.
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
