A 2-2 draw against Swansea City on Saturday meant the Carrow Road club failed to properly distance themselves from the drop zone.
And, with Aston Villa defeating Stoke City, Hughton recognises it is becoming very tight at the bottom of the table.
"It is getting tough," the Norwich boss told Sky Sports. "But we know all the teams around where we are are all capable of winning football matches.
"We have to make sure that in this final six games of the season, of which three are at home, we get enough points.
"And if we show enough belief and confidence, like we did today in good phases, then we will have done enough."
Michu had given Swansea the lead before Norwich roared back either side of half-time through Robert Snodgrass and Michael Turner only for Luke Moore to equalise.
Depending on results on Sunday, Norwich could consequently find themselves just two points clear of the relegation places.
But Hughton is continuing his belief that home form could save his side ahead of games against fellow strugglers Reading and Villa as well as West Bromwich Albion.
And with tricky away trips to Arsenal, sinking Stoke City and a final day visit to Manchester City also on the horizon, Hughton said: "Whether it is this stage of the season or the start of the season, you are always looking at your home form.
"We are tough to beat here. We have got three very difficult games away from home. Whether it will come to our home form, we will have to see."