Scott Hogan's 36th-minute goal proved decisive with Bury unable to make numerical advantage count after Peter Vincenti's dismissal for a second bookable offence soon after.
And Blackwell hit out at Rochdale's rough-house tactics along with Boyeson's policing of the game.
"Rochdale were lucky to have 10 men on in the end because some of their tackling was outrageous," Blackwell said.
"Keith Hill had a go at the referee at half-time, screaming in his face, and for me that showed in the second half. Hilly has done his job, I'm just disappointed with the officials.
"There was a point at half-time when I was worried we didn't have enough ice in the dressing room. It's up to the referee to sort that out, otherwise it becomes a free-for-all.
"But having said that we didn't do enough with the ball and that concerns me. As good as our strikers have been lately, they weren't good enough on the day.
"It's our own fault because we had enough possession. Our frontmen were nowhere near bright enough and I gave someone a job to do at a corner and he didn't do his job and the ball ends up in the back of the net.
"We've been going well but people passed on their responsibilities here. There's always something to bring you down to earth and that's what happened to us."