With eight games remaining, Norwich sit four points clear of the bottom three but the three sides directly below them all have games in hand, and could yet drag them deeper into trouble.
Hughton has seen his side win just once in their last eight matches but he remains optimistic that they can survive, even though they face Liverpool, Manchester United, Chelsea and Arsenal in their final four matches of the campaign.
However, the 55-year-old insists Norwich will go into that crucial run of fixtures believing that they can spring a surprise.
"I don't think you can ever feel we cannot get points in those final four games," he told the Eastern Daily Press.
"If they were in any other stage of the season we would not be going into them with a defeatist attitude and particularly at home, we are capable of winning against what are regarded as the bigger clubs."
Hughton also admitted the Canaries must raise their game to ensure they collect points and stressed that his players are well aware of the task ahead.
"The players know, and I will tell them, if our level of performance does not improve we will make life very hard for ourselves," he added.
"It is only ourselves who can get us out of this and we have to do that very quickly. "You have to remain focused, retain that belief but there is no doubt we are in a difficult position."