McCoist's men will be trying to record their 21st consecutive victory in a competitive match when they take on Stranraer on Boxing Day.
The run the Light Blues are on at the moment is their best since the Second World War - and could soon be their best ever.
Their all-time record for successive triumphs in national tournaments is 22 - a feat they achieved way back in the 1898/99 season.
McCoist has, like all Rangers supporters, been delighted at how swiftly his new recruits have found their form at Ibrox, particularly as the 2013/14 campaign has been played out amid an unsettling backdrop of serious unrest in the stands.
But he confessed he has been taken aback at the way the eight free agents he secured the services of in the close season have fitted in.
McCoist said: "There is far more pressure on you to win football matches at Rangers than there is at most other clubs. Most of the players we brought in during the summer had no experience of that, but they have risen to the challenge magnificently.
"As I have said before, I honestly don't think we will go through our league campaign unbeaten. I think we have been lucky to win on a few occasions this season.
"We have got a lot of difficult games coming up. The matches away from home are particularly difficult, but the lads deserve a great deal of credit for how they have conducted themselves and how they have played this season. They have been excellent. "It has surprised me how well they have adapted to life at Rangers given how much more pressure is on you here than at other clubs."
Meanwhile, McCoist has thanked the Rangers fans for the backing they have given him and his players throughout 2013.
Despite completing Stage One of "The Journey" by winning the Third Division last season and enjoying fine form this term, it has been another turbulent year off the park for the Gers.
Growing disharmony among Light Blues followers resulted in several senior officials leaving and came to a head at an often bad-tempered AGM last week when the board was re-elected.
McCoist, though, has been grateful for the unstinting backing the fans have shown his team on the park in the last 12 months.
And he is hopeful it continues in the months ahead, despite veiled threats by some fans not to buys season tickets and official merchandise if their concerns about the running of the club are not addressed.
He said: "Our supporters have been fantastic for us all year. Wherever we have gone, to whatever part of the country in whatever weather, they have been there in numbers.
"The players and the coaching staff at the club have all appreciated the support we have received throughout the year. I would ask all of them to continue to get behind the players in the year ahead because the team needs their backing."