The St James' Park victory over third-placed Forest left the Magpies 13 points clear of Billy Davies' side, who have just six games left to play.
Indeed Newcastle, who have a game in hand, could even go up on Saturday if they win at Peterborough and Forest lose at Bristol City.
However, Hughton is concentrating only on the three points up for grabs at London Road - and will allow events elsewhere to take care of themselves.
Hughton said: "It's that close. We are where we are and we thoroughly deserve to be where we are and if it happens on Saturday, then no one will be more delighted than me.
"But the most important thing is we have to win first."
Hughton, who insisted the squad would not be taking celebratory champagne with them to Peterborough just in case, saw the Magpies take a significant stride towards the Premier League as second-half goals from Shola Ameobi and Jose Enrique - the first of his career - were enough to secure victory over Forest.
The win extended Newcastle's lead over second-placed West Brom to four points and they now need just two wins to ensure their stay in the Championship lasts for just one season.
Hughton said: "Because of the timing - we are so close to the end of the season - and it's against a side who have pushed us for a large chunk of this season, it's a big win for us.
"The nature of our business is you have to enjoy the wins and it will be a nice day at the training ground on Tuesday.
"I'm quite sure everybody will have a spring in their step. But we very quickly have to bring them back down to earth.
"It's an away game on Saturday which we have to make sure we prepare correctly for.
"If we are able to take a spare chunk of what we had into that game then we have got a good chance of coming away with a victory."
The Magpies started brightly on a pitch soaked by torrential rain and might have gone ahead with just 12 minutes gone when striker Andy Carroll forced a good save from Forest keeper Lee Camp with a left-footed volley.
However, it was substitute Ameobi who finally broke the deadlock 19 minutes from time with a sweetly-struck left-footed drive, and the victory was secured in stoppage time by a rare goal from Spaniard Enrique.
Forest boss Davies was quick to concede that Newcastle will be playing in the Premier League next season, but refused to rule out his own side's chances of joining them.
He said: "I'm not admitting defeat, I am saying I think Newcastle United, in my opinion, will finish the job.
"We've got a challenge for second place that is very much still on the go."
Source: Team Talk