BOSTON UNITED 1, SHAKERS 1: A 90th minute goal by Weatherstone robbed Shakers of three points at bottom club Boston United.
Jon Newby put Shakers head just after the interval.
Full report and reaction on Monday
Bury boss Andy Preece said before the game that too many individual and collective mistakes could scupper any promotion hopes his side harbour.
In the five games of the new campaign the club have conceded nine goals and that's something Preece isn't willing to put up with.
The situation came to a head at Gigg Lane on Monday afternoon when, after going into a four-goal lead, Shrewsbury's former Bury striker Nigel Jemson struck back with three goals in the space of eight minutes.
Fortunately, the Shakers held on to take all three points, but it's that kind of profligacy that the Shakers chief and his players will be working hard to eradicate.
"We can't keep conceding the number of goals we have or it's going to cost us in the long run," said Preece.
"Conceding two goals a game is relegation form, not promotion and it's something that needs sorting out quickly.
"Once we get it right we will shoot up the league, its just discipline and communication that is the problem.
"We've done plenty of work in training this week, but it's all about keeping it tighter on the pitch during matches.
"Ironically, against Shrewsbury, we defended better once they pulled it back to 4-3 and they never had a single chance after their third goal. But all through the match I felt we should have been tighter."
With the manager's thoughts turned to defensive problems, at least he has the consolation that at the other end of the field things seem to be on the up.
At long last goals are beginning to flow as seven in the past two home games proves.
And those four against the Shrews will have given Preece some positives to take from Monday's game, a match that extended the Shakers unbeaten run to three.
"The football we played was good and I am delighted with our forward play," he said.
"The pitch didn't help us as it was sticky, so I asked the players to be more direct after half-time.
"Within ten minutes we'd scored three more goals, so I was pleased the lads had taken that on board."
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