Having opened the scoring through Bevis Mugabi at Fir Park, Motherwell had a penalty claim for handball against Rangers defender Leon Balogun turned down by referee Nick Walsh.
The match was turned on its head when Rangers scored twice in the closing minutes of the first half before romping to victory after the break as Motherwell were reduced to 10 men with the dismissal of captain Stephen O’Donnell.
“I thought we used the ball well and created chances and could have had a penalty at 1-0,” said Alexander.
“I just thought it was about these moments in games which have happened this season and been big, game-defining moments. The two goals before half time did that and obviously the red card.
“What happened after the red card, you just sit in your box and get everyone behind the ball or you try to salvage something. We tried to salvage something but obviously we didn’t have enough on the pitch to do that and they punished us when they could.
"I've not spoken with Stephen. He was quiet afterwards, as everyone was in the changing room. But I don't think now was the time for talking.
"We need to let our emotions go down and let our heads clear. This game is gone. I don't think it'll just disappear into the dust - it'll be at the back of our minds for a while - but there are a lot of challenges ahead."