The Canaries established a 2-1 lead with goals from Robert Snodgrass and Michael Turner, only for Luke Moore to snatch a point with 15 minutes remaining of an entertaining match notable for both teams' madcap defending.
It was the hosts' fifth draw in their last six home matches, leaving them only five points above the bottom three with six games remaining.
"We wanted a win but nothing changes, we still have to get enough points from the six remaining matches to make sure we're secure," Hughton said.
"But all the teams around us are capable of winning games so we need to make sure we get enough points from the last games to make sure we're ok.
"We're at the part of the season that makes everyone that bit anxious and you have to have belief in the players."
Swansea dominated the opening 40 minutes and led through the otherwise wasteful Michu, only for Norwich to claw their way back into contention through Snodgrass.
"Their camp might look at it a little bit differently, but I thought on the balance of play it was a fair result," Hughton said.
"I couldn't fault the team for their endeavour, we got ourselves in scoring positions but unfortunately we conceded two soft goals.
"We spoke about the goals we conceded, which I felt were poor to concede, but we gave ourselves opportunities to score and that is what we have found difficult."
The draw ended Swansea's three-match losing run and manager Michael Laudrup felt it was just about the right outcome.
"Ending the losses is good, but it's harder for me to answer whether I'm satisfied with one point," he said.
"We dominated completely the first 30 minutes, we were 1-0 up and maybe should have been 2-0 up.
"We allowed them into the game out of nothing, but showed character to come back and score the second goal.
"Michu had a few chances, including the one at the end that could have been the third goal.
"Am I pleased with one point? We could have won, but we could have lost too."
Norwich captain Grant Holt was lucky to escape punishment for a nasty-looking challenge on Chico Flores that saw him stamp down on the defender's shin.
"I don't know how bad the stamp was. People have said to me that he carried on playing so it couldn't have been so bad," Laudrup said.
"But you have to remember Chico has just returned after seven weeks out because of injury.
"I don't know if the card should have been yellow, red or pink. The most important thing for me was that it wasn't serious to Chico. He's in a little pain right now, but he can walk."