McNally cast doubt over Hughton's future in an interview with a local newspaper earlier this month, and was captured shedding a tear by television cameras following Norwich's 1-0 victory over Tottenham on Sunday.
But Hughton said that McNally had recently suffered a family bereavement, and that this was likely to have played a part in his emotional reaction to the result.
"I have been told (about McNally's crying), 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," he said. "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."
Referring to McNally's interview, Hughton insisted that he was not concerned by the comments made, which included that Norwich would be "almost delinquent" not to be aware of alternative managerial candidates.
"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," he added.
"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."
The win against Tottenham lifted Norwich to 14th in the Premier League.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
