Kevin Blackwell believes Bury are lacking belief after a Nicky Adams injury-time winner left the Shakers without a win in 11 league games.
Crawley looked in control after goals from Adams and Hope Akpan put them 2-0 ahead nine minutes into the second half. But Bury scored twice in the space of three minutes through Tom Hopper and Andy Bishop to put the match on a knife-edge.
Blackwell said: "With 28 seconds to go we conceded the winning goal with what was meant to be a cross. It was a fortuitous goal and that makes it painful.
"That is hard to take. When you are down there you get kicks in the teeth all the time and it showed in this game.
"Crawley showed they had the tenacity to keep going and fair play to them, but having pulled back to 2-2 we should have taken something from the game.
"There is a lack of belief and it's about having courage. Unfortunately, if it can go wrong for us at the moment it will go wrong."