An 18-yard strike from Gary Phillips in the 90th minute proved too much for Gunnar Nielsen to stop and sent the Coatbridge side into the fifth round of the William Hill Scottish Cup thanks to a 1-0 win at New Douglas Park.
Rovers had never beaten Motherwell outside the Lanarkshire Cup in 34 previous competitive matches and McCall found the defeat hard to swallow.
The former Everton, Rangers and Scotland midfielder said: "I've been very, very fortunate in my life, certainly in my football life for 34 years now, I can't recall being on the end of an upset anything like that.
"I know they happen in football and you see them happening and you think hopefully that will never come to your door. But it certainly came today and I take full responsibility."
McCall turned round to hold his hand up and acknowledge the anger of Motherwell fans who left in audible disgust after Phillips had struck.
He said: "What can you say to them? They are right to have a go. It's one of the worst results we have had. I've been very fortunate since I've been at the club to have had loads of highs.
"Obviously there are disappointments too but this is the worst. You can't do anything but apologise because it's an embarrassing result for the club.
"To be honest I would rather sit here and speak to you for a few hours because I don't really fancy going home and speaking to my family or my friends because it's horrible. There is no getting away from it."
McCall admitted he found it difficult to have a go at his players for their effort. Motherwell could not break down stubborn opponents and only tested goalkeeper Neil Parry once, when he saved John Sutton's close-ramge header following a 78th-minute corner.
When asked to explain the defeat, he said: "It wasn't down to a lack of fight and lack of desire, which is probably the worst thing that can ever be labelled at a team.
"It was just down to lack of quality. Give Albion Rovers full credit for the way they defended but our possession was woeful at times.
"We had plenty of it and we just couldn't break them down.
"When teams sit in like that it can be difficult but you have to find a way and, with the quality of player we had on the pitch, to create as little as we did was hugely disappointing."