Cooper's side led 1-0 at half time through Jon Stead's penalty, but the Bees struck three unanswered goals in the second half to clinch all three points.
"You could probably say there was six or seven from our strongest team not playing and we managed to come out with a 3-1 victory," said Allen, who was in charge at Meadow Lane from 2011 to 2012. "I would say it was a very comfortable victory.
"In the second half (the Notts players) offered nothing. They turned their back on their club. I think they let all their supporters, their manager and everyone down from the way they played.
"Obviously I've got an interest in that club because I worked there and I've got very fond memories of my time there.
"But that performance… whoever's picked those players or bought those players or got those players in, needs to take a long, good, hard look at themselves, I think."
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