The Third Division side had their hopes of causing a Scottish Cup upset dashed with only 15 seconds on the clock after Johnny Russell scored the first of his brace.
Jon Daly netted in between as United, always looking a yard sharper, eased their way into the last eight without their opponents troubling them too much.
The Glasgow team had four players with top flight experience, and McCoist believes they failed to rise to the occasion.
McCoist said: "It was certainly poor. Probably our bigger SPL players should have done better today.
"I don't think it would be any good for me to be critical of individuals at this moment in time but I do take the point.
"It was a disappointing day for one or two of the boys who, with SPL experience, would hopefully have done better.
"When criticism is due and warranted, believe me, they get it. Some of the players got it today after the game."