Peters cited the lack of composure for the problems, saying the Shrews allowed Bury to dictate the nature of the game.
He told ShrewsWeb: "We didn't do well - didn't play and got involved in the hurly burly of Bury's game and didn't play our game."
Peters said that taking chances was also a key issue: " If Mark Stallard had put the chance away it could have been a different game, if it goes in then we are on the up and may have finished (the game) sharper.
"When you have chances you've got to put them away, we didn't against Rochdale and we didn't today and that's something we've got to put right."
Jamie Tolley again looked out of sorts on the right of midfield and this could bring about changes for Saturday's hosting of Northampton.
New signing Richard Hope is looking for his first start after seeing Gavin Cowan out for eight weeks after a clash with Boston's Jason Lee on Wednesday.