Carlisle made hard work of beating League One's second-bottom side. They led through Lee Miller's penalty and Matty Robson's strike in the first 10 minutes, but Steven Schumacher sparked a Bury response in the second half, which left Shakers feeling distinctly short-changed.
After his side had dominated the second half Blackwell said: "There is only so much you can do as a manager and we're crying out for the missing pieces in the jigsaw.
"There's not much wrong with the team, but we don't have control of what is happening at present."
Six points from the holiday programme have helped drag Carlisle away from the relegation struggle, but for a weary Bury outfit the defeat at Brunton Park left them further in trouble.
Blackwell added: "When you concede goals like that and miss chances when you have had 60% of the game you get what you deserve and we got nothing because of that.
"We dominated the second half and it beggars belief the goals we conceded. We should have won the game, but we have dominated at most places and haven't got the players in the two boxes, it's as simple as that.
"Carlisle will accept they rode their luck towards the end, and it's the same situation time and time again. I feel for the players, but it's no good feeling sorry for yourself.
"The policies in the summer left us in terrible shape and half the side is loan players and young kids. We are embargoed and can't do anything at the moment.
"Tom Hopper is a tired player and it's on his mind at the moment. He had five or six chances and needs a rest - some of the players are crying out for a rest."