A crowd of 44,380 packed into Ibrox to watch the Light Blues ease to a 4-1 win over Brechin City in their Scottish League 1 opener.
The fans demonstrated their support for McCoist with chants of 'Super Ally' as Rangers bounced back from last week's shock League Cup exit to Forfar.
"They have been great to me," said McCoist. "All that does it make you more determined to do your absolute best for them."
A section of the support also voiced their unhappiness at Charles Green's return to Rangers as a consultant, with one banner declaring: 'Red, White and Blue. No Green in Rangers.'
McCoist hit back at Green in an angry post-match blast last week but was more diplomatic after today's game when asked about the Yorkshireman.
He said: "That's not my department. My department is the football team. What I would say is, once again, our supporters turned up in quite unbelievable numbers and supported the team, again, from start to finish.
"They have been the lifeline of the club for 140 years but certainly when we really needed them in the last two years. They never cease to amaze us.
"All I asked from them during the week was to give the team continued support and they absolutely did that."
McCoist was also boosted by the sight of Rangers great Sandy Jardine - who has been battling cancer since last year - unfurling the Third Division flag ahead of kick-off.
He said: "I can't tell you, from a selfish point of view, what a boost that gave me - and gave everybody.
"It was absolutely brilliant to see him. For what he has been through, he is looking absolutely tremendous.
"He said it was a great honour to unfurl the flag. I think it was a great honour for us to have him unfurl the flag. It was wonderful."
Chris Hegarty, Nicky Law, Ian Black and Dean Shiels all scored for Rangers with Steven Jackson netting a superb overhead kick for Brechin, who had Paul McLean sent off late on.
A transfer embargo means Rangers are unable to register their eight new signings until September 1, although those who played with Scottish clubs last season can feature as trialists in league matches.
Law and Jon Daly were given the nod today, after impressing in the first round of the Ramsdens Cup against Albion Rovers a couple of weeks ago, having been ineligible for the clash with Forfar.
McCoist said: "They are two big players for us on and off the park. They train hard, they work hard, they are a great example to the younger boys. They are the type of people we want at the club.
"The two lads definitely made a massive difference to the team when you look at last week's performance."
McLean was dismissed for a foul on Andy Little in the box, with the game at 2-1, and Brechin boss Ray McKinnon said: "It was a disappointing decision from the ref according to my players.
"They are saying there was nothing in it. It was definitely a game-changer. Rangers got their swagger back and killed us off with a great goal.
"The penalty decision was disappointing but that happens in football and we can't grudge Rangers their victory - they were the better side by far."