With 13 minutes remaining the big defender threw himself at David Templeton's cross and, as he glanced the ball into the net, he also bundled keeper Neil Parry over the line.
Fans around the ground looked at the ref to see what call he was going to make, but he awarded the goal.
McCoist said: "If you look at Mohsni when he jumps he hasn't got any idea where the goalkeeper is, it hits his head and it goes in. It's a goal for me.
"I think the easy decision for the referee would have been to award a free-kick. I haven't seen it again, but I thought he was very brave to give the correct decision and obviously we are relieved we are still in the cup.
"For 70-odd minutes we weren't going to be in the cup, but we kept going and got the goal so the main feeling right now is relief.
"Albion Rovers defended very, very well but on pressure we certainly deserved to take something out of the game.
"We had massive amounts of possession which we knew we would have but we lacked a little bit of urgency in the final third of the park.
"But we now have another game where we have an opportunity to get into the semi-finals which is fantastic because for long periods after the goal there was an anticipation and a sense it might not come, but we got it.
"I've had a look at the draw, obviously, but I think it would be totally wild of me to have the audacity to look forward to a home tie against Dundee United.
"We've now got an opportunity to win the league championship on Wednesday and then another game before we can think about the replay."
McCoist's decision to move Mohnsi into attack with 75 minutes played proved pivotal as he went on to nod home his side's goal.
The manager added: "We just felt the big fella would cause a bit of havoc in the nicest possible way. So we just thought he would give us a goalscoring threat."
McCoist, meanwhile, believes it is disrespectful to Rovers to say it is 'embarrassing' Rangers face a replay.
He said: "As I keep saying, I think people are maybe getting carried away with where our club is at this moment in time and the team.
"I think it's highly disrespectful of people to say that and I'm certainly not going to say it."