Defender Tom Lees headed the only goal of the game for the Shakers, who finished with nine men following the sending off of Damien Mozika in the first half and Efe Sodje in the second.
Albion also had Sam Winnall sent off in the 62nd minute for a foul on Steven Schumacher in an incident Peschisolido described as a `bizarre decision.'
"I'm delighted with the performance. The boys worked ever so hard, they were superb and I thought they nullified everything Bury had," said Peschisolido. "Fight, spirit, everything was on our side except for a very bizarre decision when Sam Winnall was sent off.
"I can't see how that was a red card in a million years. You see referees even things out and for me, that's what he did. It's ridiculous. I can't say too much because I'll probably get in trouble but no way in hell was it a sending off, or a yellow card even."
The Canadian added: "Apart from a couple of shots here and there and some half chances, they didn't really get going. I think their supporters were booing them because they didn't have anything. So it's frustrating we didn't get anything today. I'm disappointed."
Source: PA
Source: PA