The Canaries edged past Tottenham 1-0 at Carrow Road on Sunday to claim just their second league win in 12 attempts.
Under-fire Hughton earned himself yet another stay of execution as Norwich manager with Sunday's win, which lifted the Canaries four points clear of the relegation zone.
Chief executive David McNally's revelation last week Norwich would be "delinquent" not to cast around for potential managerial replacements has heaped further pressure on Hughton.
The former Newcastle boss shrugged off all the stress in the wake of Sunday's victory, then refused to pinpoint a points tally to ensure Premier League safety.
"We've all got our own private thoughts, but you almost don't want to start thinking that way, because nobody really knows what it will take," said Hughton.
"Sometimes it's better to think that way, because it makes you want to go into every game making sure that you give yourself the best chance of getting the result.
"As much as I can say to you that it's about our results, of course you're always looking at the results around you, hoping that they go well for you.
"But for the one weekend they might go well for you another weekend they won't, so we've got to look after our own."
Robert Snodgrass' cool finish secured victory over Spurs, with Hughton praising his players for their upbeat and confident approach through testing times.
"We all accept that we're getting into that vital part of the season where every result seems to be a big result," he said.
"We've certainly been very good for the last three games before this.
"That's a wonderful standard to see.
"What we need to do is alleviate a little bit this pressure on ourselves, by getting the goals that can do that.
"It's tough against the likes of Tottenham, but we just need to relieve a little bit more pressure on ourselves.
"What gives me confidence is we have a really good group of players.
"The training ground is a really good place to be, they feel it and they are as frustrated as anybody."
Norwich travel to Aston Villa on Sunday, where victory would propel them above the Villa Park men in the Premier League table.
Goal-shy striker Ricky van Wolfswinkel produced a neat intervention to steal possession and set up the move that led to Norwich's winner against Spurs.
Hughton is now hopeful his £8.5million summer signing can start to repay that hefty price tag in goals as well as graft.
After scoring on his Premier League debut van Wolfswinkel has now gone 19 Norwich games without a goal.
Hughton admits if that barren run ends, his side will pull away from the relegation scrap.
"It's been difficult for Ricky, but his performance on Sunday, that's how he started the season, where he gave us good legs up front, working the channels in behind," said Hughton.
"At times Tottenham play a high line and we felt his maybe his running ability could just get beyond them.
"Every striker wants to score goals, and being out injured for three months in your first season at a new club in a new division, it's tough.
"But I'm really pleased for him, for how he went."