Hughton was dismissed from Carrow Road on Sunday night with the team five points clear of the relegation zone in the Premier League table.
Under-18s coach Neil Adams has replaced the 55-year-old for the final five games of the season.
Despite widespread bewilderment following Hughton's departure, McNally believes that Norwich's recent form warranted a change of coach.
"We felt we were left with no choice," he told reporters. "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."
Norwich continue their bid for survival on Saturday when they travel to fellow strugglers Fulham.