Despite having home advantage, McCoist's team entered fresh territory with his first quarter-final in major domestic cup competitions as a manager.
And Rangers required a controversial late equaliser from Bilel Mohsni to cancel out Ciaran Donnelly's cushioned volley on 14 minutes.
Rovers felt aggrieved Mohsni's goal was allowed to stand after he challenged for the ball with both hands above his head and appeared to barge Rovers keeper Neil Parry into the net.
McCoist, though, believes there was nothing wrong with the goal, without having viewed a replay of the incident.
"It is a goal," McCoist said. "If you look at Mohsni, not having seen it again, he jumps and I don't think he has any idea where the goalkeeper is and it hits his head and goes in.
"It's a goal for me. I think the easy decision for the referee was to give a foul but I thought he was very brave in giving the right decision.
"I am obviously relived that we are still in the cup. For 70-odd minutes we weren't going to be in the cup.
"But we got the break, got the goal and the main feeling is relief.
"I thought Albion Rovers defended very well but on pressure we certainly deserved to take something out of the game and the draw was what we got."
The reward for the winner of the replay will be a shot at top flight Dundee United at Ibrox, which will be at a neutral venue.
McCoist added: "I have had a look at the draw but as you saw today, it would be wild of me to have the audacity to look forward to a home tie against Dundee United. I am certainly not going to do that."
Rovers manager James Ward decided not to dwell on the incident that led to the goal, and opted to look at the positives.
"It's a goal, there is nothing I can do to change it," Ward said. "The focus should solely be on the quality of our performance.
"We were under immense pressure in the second half and we defended manfully at every opportunity. I have been saying all week to people that we were capable of winning and nobody believed me.
"We showed as a group how capable we are and the players deserve immense credit. It was a fantastic performance in terms of discipline and organisation."