The light issue was problematic for the second straight year in Sydney with players taken from the field on Thursday, despite the floodlights going on during day two.
Altogether 40 minutes were lost before rain prevented players from returning for the rest of the day, with 30,000 fans offering a chorus of boos at the decision.
The issue comes at a time when the future of Test cricket is being threatened due to a T20 franchise takeover.
"We are in the entertainment business," Greenberg told SEN.
"If we can put a man on the moon, surely we can find a way to get ourselves out on the field with lights and figure out some sort of technology.
"Something to both keep the players safe, ensure the battle continues in a fair and even contest, but also make sure that play continues.
"Member nations need to get together with the ICC and find a way to ensure that these things don't continue to happen.
"Now, clearly, you can't play in the dark ... but I can't think of another sport that will do this consistently, just walk off when the light is not good."
Greenberg admitted part of the challenge was getting the players on board.
Usman Khawaja argued on Thursday he would retire if a pink ball replaced a red one so it could be used under lights.
Players are insistent the pink ball reacts differently to the red one and should not replace it entirely outside of day-night Tests.
"There's no doubt that we've got a part to play in this as well," Greenberg said.
"And that's a big part of my job, to bring the players along that journey as well.
"To educate them and inform them and have some maybe some difficult or some confronting conversations. That's got to be part of it.
"It might be (a pink-ball solution) and there might be something else, but I'm pretty keen to make sure that we're not sitting here this time in 12 months time having the same conversation."
Greenberg also backed calls from CA chairman Mike Baird for global cricket funds to be better distributed to nations outside of Australia, India and England.
India currently receive close to 40 per cent of the ICC's $5 billion of revenue for global tournaments.
He believes more assistance for other nations would allow for Test cricket to remain a priority and help better pay players from nations outside the big three to keep them in red-ball cricket.
Greenberg warned if action was not taken it would be fanciful to think the number of regular Test-playing nations would not drop in the next 10 years.
"There's not a lack of revenue in the game. It's about the prioritisation of where that revenue goes," Greenberg said.
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