A crowd of 49,118 - one of the biggest in the United Kingdom - watched the Glasgow giants play their first ever home game in the Third Division.
And McCoist believes the continued backing of the support will help drive Rangers on as they continue on the road to recovery after being consigned to liquidation in the summer.
He said: "It was quite unbelievable really.
"I looked out of the office at 1:30 today and Edmiston Drive was chock a block.
"It was fantastic. It's a statement and it's really encouraging.
"When you're getting support like that from the fans, you can only go one way and we must go forward."
The Shire took a shock lead through a Paul Quinn penalty after just three minutes, before Andy Little claimed his first hat-trick for Rangers.
Francisco Sandaza also marked his first start for the club with a goal and Lee McCulloch put the gloss on the win in injury time.
On Little's treble, McCoist said: "There is always something happening when Andy is in town, that's for sure.
"He creates chances and he probably could have had another two.
"He was great and I've got no problems at all with Andy. He has bundles of energy and he makes things happen.
"We are probably playing him in a position that wouldn't be his most favoured on the right-hand side.
"He is aware, as are the rest of the lads, that it's a small sacrifice in terms of the overall team performance, which is the most important thing.
"He certainly looks as though he is going to get on the end of things."
It was an impressive showing from Rangers after a less-than-ideal opening, and McCoist added: "It was not the started that we would have wanted.
"It took us a while to get going but once we did get going I thought we were all right.
"We created a staggering amount of chances and I was very pleased with our second-half performance."
Dean Shiels was forced out of the action early on with a leg knock and is now a doubt for Tuesday's Ramsdens Cup tie at Falkirk.
McCoist said: "He's struggling. He's got an ice-pack on just now and he would probably be struggling for Tuesday. We'll see how he is in the next 24-48 hours."
East Stirling boss John Coughlin revealed afterwards that midfielder David Greenhill left Ibrox at half-time due to a family issue and paid tribute to the player for initially offering to see out the game.
He said: "His dad was in a hospice in Edinburgh. He left the ground knowing it was only a matter of time.
"I said to David at half-time to go and he wanted to play on. It shows the mark of the kid that he was willing to stay and play the second half.
"There was a member of his family here who had a word with him in private and the decision was made. He said he had to go and it was 100% the right decision."
