The veteran striker, 37, pounced in the fourth minute of stoppage time to snatch the Robins' first win in five matches, which piled the pressure on Bury, who have now lost their opening four home games despite being the better side for long periods.
"Everyone on and off the field works tirelessly for the cause," said Allen. "We've got a good group of people together and when you've got that you've always got a chance.
"We had two injuries so had to make changes, but we kept our shape and it was a solid, disciplined performance.
"We limited them to a few opportunities and didn't threaten a great deal ourselves, but I always thought we'd get a chance on the break as the game went on.
"That was the case and it was a great finish by Barry. I was happy to get a clean sheet away from home. We could have done better with possession, but it doesn't matter - we got the three points."