Greene, who averaged 28.4 disposals a game last year (eighth in the AFL), was sent to Carlton goalsneak Jeff Garlett, who booted a game-high four goals in the Blues' 94-point win.
Midfielder Dylan Shiel, meanwhile, was used as a run-with midfielder, keeping Carlton captain Marc Murphy to 22 possessions.
Coach Kevin Sheedy said all of the club's emerging midfielders would be given similar assignments as they develop to teach them to "hammer the opposition" when they have the ball.
"Dylan's learning a trade and so is Toby Greene," the coach said.
"Last year they played on the ball and perhaps were given a free run in their positions, but now they're learning tight defensive midfield pressure positions.
"It's not all about spreading offensively out of the stoppage like you might feel the freedom to when you're in the under-18s.
"They're the teachings they need at this stage of their career … every one of our midfielders is going to go into the back half and they're going to learn it."
Sheedy said Shiel had played his role well and would continue to be used as a run-with player, while Greene, who still finished with 28 disposals and five clearances, would remain at half-back.
The Giants' loss on Saturday was their 10th so far in a winless season, with their average losing margin over the last month 103 points.
First-year midfielder Lachie Whitfield, who was a strong performer on Saturday with 21 disposals and a goal, said morale among the players remained high despite the big losses.
"The last month has obviously been pretty tough and we've been coming together and having long chats about the morale," he said.
"(Captain) Callan Ward is leading that really well, keeping us all together and trying to teach us all about care for one another.
"We think that's vital on-field and is represented by things like tackles and caring for your mates.
"Even though we are losing by fairly hefty scores, the morale is pretty high."
Nathan Schmook is a reporter for AFL Media. Follow him on Twitter: @AFL_Nathan
