Rangers will play Dundee United in the last four at Ibrox, but only if they take care of Albion in a quarter-final replay at New Douglas Park, Hamilton, a week tomorrow night. United have knocked Rangers out of the Scottish Cup in the past two seasons and in three of the last four.
The draw put the cup favourites, Aberdeen, against St Johnstone in the other semi-final. That game is a re-run of the League Cup semi-final which Aberdeen won 4-0 at Tynecastle, but this time it will also be held at Ibrox. The two ties go ahead on April 12 and 13.
Only a disputed equaliser 13 minutes from time, scored by Bilel Mohsni as Albion claimed a foul on their goalkeeper, spared Rangers an almighty cup humiliation after they trailed for over an hour to Ciaran Donnelly's opening goal. "Obviously I'm relieved we are still in the cup," said McCoist. "For 70-odd minutes we weren't going to be. We kept going and got the goal and right now the overwhelming feeling is relief."
Rangers dominated but were constantly wasteful, being booed off at half-time and full-time. "We lacked a little bit of urgency in the final third of the park," said McCoist. "I thought our delivery from the right in the first half was too high. But it's another game where we have earned a chance to get to a semi-final and that's fantastic. I definitely think we would have been harshly done by if we didn't at least deserve another crack at Albion Rovers."
Mohsni scored with a back header but Albion players insisted he had raised his arms to impede Neil Parry. "If you look at Mohsni, he jumps and doesn't have any idea where the goalkeeper is and it hits his head and goes in," said McCoist. "It's a goal for me.
"The easy decision for the ref [John Beaton] would have been to give a foul. I haven't seen it again, but I think he was very brave to give the correct decision."
Parry said: "I thought it was a foul. He jumped with his arm into me and it would've been interesting if it had been the same scenario at the other end and it was to make it 2-0 for us. I don't know. I was certainly disappointed at the decision. But he made the decision and I'm not going to criticise him. I think the story should be about how well we played and how much of a shock we gave them."
Ebullient Albion manager James Ward said: "I've been saying all week to people we were capable of winning. I think no-one believed me. But we showed today how capable we are. The players deserve immense credit for what they achieved today. It's a really hard place to come to be so focused, disciplined and organised for that length of time."
Asked if he was confident about the replay, Ward replied: "Yes. I do not change my view. We are capable of beating Rangers. Hopefully some of you might come along with me now.
"But I don't think you will. We will do our best to convince you in the replay. What were my thoughts when our goal went in? I wished he'd scored in the 94th minute."
Scottish Cup. Semi-final draw
St Johnstone v Aberdeen
Rangers or Albion Rovers v Dundee United
Ties to be played the weekend of April 12, 13 at Ibrox