Coventry boss Andy Thorn could sense his side would not hold on to their two-goal lead against Bury before seeing them pegged back to 2-2.
A 25-yard screamer from Adam Barton and a powerful free-kick from Carl Baker had Coventry two-up within 28 minutes.
But the Sky Blues failed to put the game away and were made to pay. Bury debutant David Healy coolly converted a 55th-minute penalty to give the visitors a lifeline after he had been fouled by Richard Wood.
Then, following three substitutions in 13 minutes from Shakers caretaker-boss Peter Shirtliff, Bury were level when one of those replacements, Lenell John-Lewis, headed home Joe Skarz's cross.
Thorn was aware of the risks of a 2-0 half-time lead, but could not prevent his side slipping.
He said: "We told them at half-time exactly what was going to happen and it did. They matched us up, we told them that would happen and we got complacent. We knew what substitutions they would make, we know what they do in their games and that's exactly what they did. Everyone knew what they were about and we were aware of it.
"Two poor bits of defending have cost us. Two schoolboy pieces of defending for the two goals."
Shirtliff, on the other hand, was pleased with the response of his players in the second half.
He said: "We weren't in the game first half, we didn't get any possession, didn't really threaten their goal, I think we had one effort on goal.
"I had to change it around at half-time slightly and we got a foothold in the game particularly when we got the penalty. We created more problems, put it that way. I was pleased with the second half and the spirit of the boys to keep going until the end."