The Canaries head into the final six games of the Premier League season only four precarious points above the bottom three, and Hughton is expecting plenty more drama between now and the conclusion on 19 May.
There was undoubted frustration in the crowd as they drew 2-2 with Swansea on Saturday, the visitors dictating play for long spells but still having to come from behind to claim a point and deny Norwich a win that would have gone a long way to sealing their future in the top division.
They have three games remaining at Carrow Road, against fellow strugglers Reading and Aston Villa as well as mid-table West Brom, and boss Hughton hopes their home form will be enough to see them through
Hughton said: "You have a support that wants you to do well. There is always that little bit of anxiety that sets in but it's difficult. We're going to need this support now as much as at any time.
"We know we have to give them something to cheer about but they showed how much they can help during our best spells of the game.
"It is going to be a tight last six games of the season and we need to show as much determination. If we do that we have every chance.
"You can sense that frustration with the crowd because we are certainly at that period of the season when it makes everybody that little bit anxious. You have to have belief in the players and what I was really pleased about through that anxious period was the response of the players.
"They showed how desperately they wanted to win this football match and if we show the same belief and the confidence we showed in this game then we will have done enough.
"We put ourselves in a reasonably commanding position, if not in terms of possession, but then there are not too many teams who will out-pass Swansea."