Hughton's future at Carrow Road has come under scrutiny in recent weeks due to the Canaries' poor form in the Premier League.
Norwich are currently four points clear of danger with eight games left to play. However, Snodgrass believes that the board should stay loyal to Hughton by giving him the time to improve results.
"If you look at Sam Allardyce [at West Ham United] there is the proof of the pudding," the Scot is quoted as saying by Sky Sports News. "It is about faith and loyalty but let's be honest there isn't any loyalty these days.
"You see people lose their job within two months. All Chris Hughton can do is get results."
Norwich continue their battle for Premier League survival on Saturday when they play host to Sunderland.