The Carrow Road club beat Reading 2-1 thanks to two goals in two minutes at the start of the second half from Ryan and Elliott Bennett.
But Hughton will not be celebrating with his club's euphoric supporters just yet.
"I still think we have to look at that 40-point mark," he said. "It would be nice if we were at that now, but we're not. We've got four games left and I still think we'll need more points.
"We talked about these last five games and finishing the season well and we've started that today."
He continued: "If we'd lost it would have made it more difficult. Maybe then more anxiety sets in.
"We've got good sides around us capable of winning games and thankfully we've done that today."
Hughton admitted Ryan Bennett's opener had been a huge relief.
"Reading had little periods where they did well, but goals change games and we got ours at the right time," he said.
"It was a big goal because it got rid of the nervousness and getting the second goal so quickly afterwards got rid of it more.
"The only disappointment was allowing a side back into a game that I thought they had no right to."