Barker left the Shakers on the eve of the season to take charge of the Red Devils and successor Blackwell made the scathing assessment after their 1-0 home defeat to Swindon on Saturday.
This weekend sees the two men come face-to-face when Crawley travel to face the side bottom of the table and without an League One victory to their name, although Barker points to his achievements last term to demonstrate that Blackwell is wide of the mark.
"We finished 12th in League One with that squad last season," Barker told Crawley News. "I don't agree with [Blackwell's] comments.
"I found the squad easy to work with, there is a great bunch of players there. That squad was in the top 10 last season with one of the smallest budgets, so I don't think what he's said is right."
On the forthcoming Gigg Lane clash, Barker added: "We don't get any more points for beating Bury than we would any other team , no matter what everyone thinks. I know exactly what the thoughts will be in the Bury dressing room because I was there when we played Scunthorpe when Alan Knill was there. For me the only difference between this game and any other is that I know this team particularly well."