Hughton was relieved of his duties on Sunday after a 1-0 defeat to West Brom a day earlier, a result that left Norwich with four points from their last six Premier League matches.
With five games remaining, Norwich sit 17th, and although they are five points clear of the relegation zone - they face a tricky run-in with fixtures against Liverpool, Manchester United, Chelsea and Arsenal to come.
First up is a crucial clash with relegation rivals Fulham at Craven Cottage on Saturday, with youth team manager Neil Adams installed as first team manager ahead of the match.
And McNally insists a change was needed to ensure they remained in the top flight.
"We felt we were left with no choice," he said. "Recent results have been disappointing, and we were in a position where we felt there was no choice, we had to do something to ensure best chance of staying in the league
"Four points in our last six matches is not good enough, it is relegation form. It is sad to see Chris go, but we believe we have a greater chance of improving our position.
"It was a unanimous decision by the board (to sack Hughton)."
Adams has impressed within the club after guiding their youngsters to FA Youth Cup glory last season, and the job is his long term if he can impress according to McNally.
"Neil's an excellent coach, very good tactically and technically," he added.
"First things first we need to get to end of the season and cement our place in the Premier League.
"It's over to Neil now to make sure he's the manager for the long term. Results will dictate whether that happens or not."
The 48-year-old coach is relishing the opportunity and intends to mould the team into his own style before their clash with Fulham.
"I've got to put my stamp on it, organise the players the way we want to play and need to play," said Adams.
"To be offered the opportunity is an honour and privilege, and I am very confident we can get the outcome we expect.
"The key from now is getting the right game plan, get the tactics right and a system the players are comfortable with."
