Second-half goals from Lee McCulloch and Dean Shiels clinched a deserved victory for the Gers as they dumped Stuart McCall's side from the competition to book a place in the last eight.
It was the first time the Ibrox side have faced a top-flight team since being forced to start the season in the Irn-Bru Third Division.
And while the Gers boss wants his players to believe in their ability, he knows there is still plenty of hard work to be done as they attempt to make the long journey back to the top of our game.
McCoist said: "It is a wee indicator to themselves and the support that we can play from teams higher divisions.
"Also, we can't get carried away. It is a very small step on a long road.
"We are going up to Forres on Saturday and there will be a big difference to tonight.
"As good as the result was, I hope the players can see the reasons for the performance and the victory, that is the important thing. You learn things in defeat but you can learn in victory.
"It is important we look at the game and the reasons why we did a lot better. We have to see that on a far more consistent and regular basis.
"I just wanted to progress into the next round, obviously aware of who we were playing and that they are the form team in the country at the moment.
"All it did was give us an opportunity to see how we could compete against a team like. We did it very well.
"It was a good result and good performance but it gets us into the next round. We have miles and miles to go."
Rangers now join Old Firm rivals Celtic and six other SPL teams in the draw for the next round.
A Glasgow derby clash would set pulses racing across the city, but McCoist is only hoping for a home tie when the draw is made for the last eight.
He said: "An Old Firm game would create a massive, massive amount of interest, not that they don't normally.
"If you can give me a home tie, I will take that against anybody."