It was the club's first fixture at home since being placed into the third tier of Scottish Football and a capacity of 38,000 witnessed the match.
And Green couldn't be more proud of the club, telling BBC Scotland: "For me, it was a real heart-warming experience.
"It has been a night to remember. I'm so, so proud to be associated with the turnaround of the club.
"I think it was an act of defiance, but I think it's also that Rangers fans are passionate about the club.
"The Rangers fans have stood by the club and stood up to everything that has been thrown at it.
"There were days in the early part of the transaction when I was really questioning first of all what had we got ourselves into and secondly was it deliverable.
"But, if ever there was a moment where I could look back and think everything was worthwhile, it was this evening.
"Having seen the support we had today, me and my investors are behind this club, we are here to stay."
"It seems to me like the old days where there were 40,000 but only 20,000 paid and the others went god knows where."
Despite plying their trade in the third division, Rangers are thought to be paying higher player wages than that of Scottish Premier League clubs in a bid to add more players to their depleted squad, a policy Green has defended.
"We've got to get players to the club for the next two seasons before the transfer ban will come in at the end of August," he explained.
"What the manager has tried to do is put a squad together that will see us through to the end of that transfer ban.
"We have lost 21 players since February. In the Cup games, we have the chance to play against some of the SPL sides and we want to be competitive against them."
Manager Ally McCoist was equally as full of praise of the supporters as Green but also insisted good cup runs could benefit the younger players massively."That was absolutely fantastic," he said. "It was a wonderful response from everybody - players and fans.
"Our support has been unbelievable and I believe we have the best supporters in the country.
"We are ready to play anybody in the cup," he said.
"I'm really excited about the young guys. We've got three or four lads with great potential. But we need a blend, with experienced pros on the park to look after them."