The Light Blues boss was forced to demand an improved performance against League One rivals Dunfermline on Monday night after the Boxing Day draw with Stranraer robbed them of their 100 per cent record.
His players responded with a 4-0 drubbing of the Fifers at East End Park to extend their lead over the second-placed Pars to 14 points with a game in hand.
But McCoist - the club's record goal scorer - insists he should not have to worry about whether his players are in the right frame of mind to play for the 54-time Scottish champions.
He said: "It is a self-pride and a self-motivation that they have to find from within themselves.
"We can keep them going to a certain extent but it is something that Rangers players have been faced with for 140 years. You have to get yourself motivated for every game.
"There has been periods where our club has been way ahead in league competitions but they keep going.
"We owe it to the fans. You saw our fans last night and I thought they were magnificent. They were unhappy on Boxing Day and rightly so, but there were some true great supporters at East End Park and playing for them in itself should be enough motivation for our players."
McCoist made two changes to the side that disappointed against Stranraer as Lewis Templeton and Arnold Peralta were dropped in favour of Stevie Smith and Fraser Aird.
And it was 18-year-old Aird who made the most of his opportunity as he struck a 22nd-minute opener before Nicky Clark, Nicky Law and Robbie Crawford added a polish to the display.
And the Scotland Under-19s winger admitted the manager's faith is the morale booster he needed.
"I have been working my socks off in training and when I have got my chance in the team I have just tried to take it," said Aird. "I think I did that against Dunfermline as I put in another good 90 minutes and I got myself another wee goal and that is always good for the confidence.
"I was delighted with the performance and the fact that we gained another three points. The manager has shown he has confidence in me.
"I just have to show him that I am worthy of a place in the team and that I can play. It was great to round off 2013 with another goal and hopefully I can keep it up in 2014."
Even after the win over Dunfermline, McCoist refused to write off the League One title race as he announced he did not want to "disrespect" Jim Jefferies' side.
And Aird showed similar restraint as he said: "The league is not over yet. We have to just take it one game at a time and we do not look any further ahead than we have to.
"Rangers have another massive game ahead against Airdrie on Thursday away from home and we played well down there the last time we were there and another performance like that would be great."
Aird's goal was his second of the season but while he was making a claim for further first-team involvement, fellow youth recruit Barrie McKay was settling into life at Morton after being dispatched to Cappielow on a month's loan.
But McCoist insists the 19-year-old is still a firm part of his plans.
He said: "I sat Barrie down and told him he should not be discouraged. Far from it. The objective of the situation was to try and get him game time.
"So far from being discouraged he should see it the opposite way. Former Rangers players like Charlie Adam and Alan McGregor have gone down that route and then gone on to have top international careers."
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- League One