McNally announced his resignation after their loss to Manchester United on left them four points from safety.
"Nobody expected after [Sunday's] Manchester United game we would lose our chief executive," Balls said.
"It's been very destabilising to the club. But we've got to make sure going forward the football club keeps going from strength to strength."
He told BBC Radio Norfolk: "What happened after the Manchester United game, David McNally resigned verbally, then in writing, then on Twitter. It came out of the blue for all of us.
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"The directors had a discussion over the course of Sunday and decided with great regret to accept that resignation."
McNally had been at Carrow Road since 2009 when the club were in League One.
Successive promotions took them into the Premier League, and four of the last five season have been in the top flight.
But with two games to go, the Canaries are four points behind 17th-placed Sunderland, who could secure their top-flight status with a win over Everton on Wednesday.
Whatever their fate, Canaries boss Alex Neil appears likely to keep his job.
"Alex Neil is one of the best managers in British football. He's got our 100% support for this week and also in the coming months as we deal for next season," said Balls.
"But clearly it's been messy. When there's speculation all over the place, the board has to stand back and ask what's happened and what's our responsibility?"
Neil admitted he would examine his own contribution if Norwich are relegated.
Speaking at a news conference ahead of Wednesday's match, Neil said: "At the end of the season I'll be judging how I've performed, how other people have performed and I'm pretty sure people will be judging me. That's normal in the Premier League."
David McNally's resignation as chief executive has "destabilised" Norwich City, says club chairman Ed Balls.