McCall described his team's possession play as "woeful" as they struggled to break down a disciplined Rovers side before Gary Phillips struck the only goal in the 90th minute.
Motherwell only seriously tested Rovers goalkeeper Neil Parry once, when John Sutton saw his powerful header stopped following a 78th-minute corner.
Despite having the vast majority of possession and territory, McCall's team could not create chances against Rovers, who threatened sporadically before their winner, notably when Liam Cusack forced a good save from Gunnar Nielsen.
Motherwell had survived a couple of other scares but McCall was shell-shocked by the late winner, which sparked an angry reaction from some Motherwell fans at New Douglas Park, although many applauded the League Two side off the park.
McCall said: "It's going to be a hell of a long week but once the dust settles we have got to look forward.
"We are actually doing okay in the league and we have got Celtic to come to us on Friday night. Between now and then there is going to be a lot of soul-searching and analysis and (looking at) what we can do better.
"But it certainly wasn't down to a lack of preparation. We had Albion Rovers watched four times, I had seen a DVD, and we had profiles of all their players up on the wall before the game. We talked all week about approaching the game properly.
"I don't think we did approach it in a casual way or a negative way or 'thinking this is going to be easy' way. I just think the quality of our passing and crossing was probably one of the worst since I've been at the club."
McCall, whose side missed a chance to equalise in injury-time when Henri Anier sliced wide, added: "But I don't want to take anything away from Albion Rovers.
"They defended manfully and gave it their all. I said before the game they would match us for energy, aggression and desire and hopefully our quality would come through.
"It didn't. We didn't have the nous or intelligence. We changed the shape a few times to get in behind and our final ball let us down.
"I said at half-time, 'Just improve on the tempo of your play', and it just didn't materialise.
"After the game it was more silence than anything else. It was just numbness."
The victory was the Coatbridge club's first against their Lanarkshire neighbours in the 35 meetings between the teams in major competitions.
Rovers boss James Ward was delighted with the way his side learnt from their 4-0 defeat by Rangers in the Ramsdens Cup by maintaining their concentration and discipline.
Ward said: "You wait long enough to play against teams like Motherwell and Rangers and sometimes what happens is people let it pass them by.
"What I said to them was, 'Don't have any regrets coming back in about what you might have done. Give us everything you have got and if that means there is 30 minutes to go and someone else needs to come on and do their bit, then that's fine'."
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