Illingworth is scheduled to transfer to the third umpire's box for the final test in Christchurch starting on Saturday and, despite the umpire's devastation over the farce that took place, Broad made it clear there was nothing in the rules of the game that could overturn what was simply human error.
"Unfortunately Richard was distraught afterwards when he realised that it wasn't a no-ball," Broad told News Corp.
"I think when anyone is proved wrong in any decision that they make it's clearly embarrassing at the time. But umpires, particularly on the elite panel, have a great ability to be able to overcome that feeling and get on with the game.
"There can be nothing done about it.
"The problem is that when an umpire calls a no-ball, you can't change that decision because under the laws a batsman may change his shot when the no-ball is called. It was called - that's the end of the matter.
"Richard is a Yorkshireman, he shrugs his shoulders and gets on with it. I'm constantly amazed at how the umpires, when they do make their occasional errors, are able to recover from it."
There have been reports that the Black Caps were livid with the decision and the fact it came so soon after they were robbed of victory - and a drawn series - in the Adelaide test earlier this summer.
On that occasion a DRS shocker by third umpire Nigel Llong cost the Kiwis a giant lead in the match. In Wellington they were forced to watch on as Voges turned his slice of luck on seven into a game-defining innings of 239.
When asked if he'd had an angry Black Caps coach and captain come to him over the matter, Broad said: "What goes on in a dressing room remains in the dressing rooms but I'm sure ... [they're] human beings."
Brendon McCullum had earlier remained tight-lipped over the controversy other than to say he was "disappointed".
No official complaint has been lodged by New Zealand and Broad played down the issue of standing umpires calling no-balls as being a major problem for the game - claiming controversies are one small downside of the overwhelming positive that is modern television coverage.
"What can you do? Change the laws? I don't know, possibly.
"But under the current laws and playing conditions it's what it is and players as well as spectators and media and other officials have just got to go by what is done on the day.
"It's been part of cricket ever since cricket started.
"Errors from players and match officials happen.
"I don't know that it's getting any harder [for umpires to call no-balls]. I think what is different is the media are so much closer to the action now out in the middle than they've ever been in the past. Therefore, they're showing up good things as well as bad things in the game.
"The coverage of cricket nowadays is absolutely fantastic - it brings the game into people's homes and you've only got to look at the television viewer figures in Australia for Big Bash - it's been fantastic.
"There are obviously good and bad things in every department, you've just got to accept what goes on."
- Sydney Daily Telegraph
