McNally was pictured in tears at the final whistle of Sunday's nervy victory, the stress of a relegation battle exacerbated by the death of a close family member understood to be his father.
McNally last week admitted Norwich would be "delinquent" not to be casting around for alternative managerial candidates, sparking rumours Neil Lennon has been lined up to replace Hughton should Norwich continue to struggle.
Robert Snodgrass' second-half goal saw off Spurs and edged Norwich four points clear of the relegation zone.
Hughton admitted he hopes Norwich's "best performance of the season" could help save his job and keep the Canaries in the Premier League.
"I have been told (about McNally's tears), but I can also tell you that he had a bereavement in his family, I think yesterday and I think that's had a fair bit to do with it," said Hughton.
"I speak to the chief executive on a very regular basis, we speak about lots of things.
"One thing I can guarantee is that everyone is pulling in the right direction here.
"As manager of this football club you have to go with the ups and downs, the disappointments and the highs, and you have to get on with your job.
"You have to do what you have to, and that's get the best results you can.
"I think perhaps what I accepted was that it was a very long interview, and of course there were an awful lot of positives that were said in that interview that were ultimately not picked out.
"Part and parcel of the game is you have to get on with the job, and ultimately you'll always be judged on results, and that's very much what we're doing here."
Midfielder Snodgrass fired only Norwich's 12th home league goal of the season, and that proved enough to secure a second win in 12 Premier League games.
Tottenham produced a strong second-half fight back, but were left to lament replacement Roberto Soldado wasting two clear scoring chances.
"This season, this would be our best performance I think," said Hughton.
"We were very good at Stoke away, we were very good at Chelsea, and Man United for 45 minutes was arguably our best.
"We all accept we're getting into the part of the season when the pressure's on.
"We've certainly been very good for the last three games.
"That's a wonderful standard to see.
"We just need to alleviate a little bit of this pressure on ourselves, by perhaps getting the goals that can do that.
"What gives me confidence is we have a really good group of players who work hard, and the training ground is a good place to be.
"They feel it and they are as frustrated as anybody.
"It's a good place to be, certainly when you're getting good results.
"This performance underlines that they care, and they are desperate to make sure they are Premier League players next season.
"First and foremost they will work hard each day, that's their responsibility, they want to do well and they want to stay in the team.
"That has to be their drive."
Liverpool's 4-3 Anfield victory over Swansea leaves Tottenham six points behind the Reds in fifth place.
Manager Tim Sherwood admitted Spurs now face a battle to overhaul their Merseyside rivals for a fourth-place finish to secure Champions League football next season.
Admitting the gap between Spurs and Liverpool is now considerable, Sherwood said: "It looks big, it's a real blow to us but we've got to bounce back.
"We've got the second leg of the Europa League match and then we've got Cardiff at home.
"We need characters in the dressing room to be able to do that.
"We can't use Thursday's game at Dnipro as an excuse, especially as we were stronger in the second-half.
"We created a few chances after going behind, but we just couldn't take them.
"It's the first major setback I've had as manager, and now the players must respond."
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