Hughton was sacked on Sunday, a day after his side slumped to a listless 1-0 home loss to West Bromwich Albion, a result that left them five points above the drop zone, having lost four of their last six Premier League matches.
He has been replaced by youth team coach Neil Adams, who made more than 200 appearances for the club on the right wing but has not managed at senior level.
McNally said Hughton, 55, "is one of the good guys in an industry where you swim with sharks" but it was the unanimous decision of the board to let him go.
"Clearly it's a results business and four points from the last six games, particularly against peer-group clubs, hasn't been good enough," McNally told a news conference on Monday.
"Seven away defeats consecutively, four defeats in six games, four points in six games is relegation form."
The 48-year-old Adams said it took him about "two seconds" to accept the job, despite the magnitude of the task awaiting him.
"I've got to put my stamp on it, I need to organise the way I want the players to play," he said.
"More than anything we need a bunch of players prepared to do absolutely everything.
"People outside Norfolk will not realise how big a club this is. We need to send a team out to win a game.
"Am I confident we can get enough wins to stay up? Absolutely.
"I was approached on Sunday and it took two seconds to make the decision. Everyone knows what this club means to me. I'm looking forward to doing the job with relish."
Despite their precarious position and the tough fixtures to follow, Adams said extending Norwich's stay in the top-flight to a fourth consecutive season did not hinge on getting three points against Fulham.
"I don't think it is a must win," he added.
"But if we win on Saturday it helps our cause. But there are four other games and we can win against the bigger teams. But we're going to Saturday's game to win it and we will deal with the consequences afterwards."
McNally said results would dictate whether Adams would remain in the role after this season.
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