Peter Houston insisted Falkirk will not deserve to finish second if they defend as poorly again in their final league match of the season.
Queen of the South striker Stephen Dobbie ruthlessly exploited their deficiencies, opening the scoring in nine minutes and grabbing a leveller 12 minutes from time.
Falkirk manager Houston said: “If we are going to lose goals like that we’re not going to get second place – and we don’t deserve it if we defend like that.”
Dobbie gave Queens the lead in nine minutes when Falkirk fell asleep at a throw-in and Lyndon Dykes set him up for a tap-in.
Nathan Austin drew the Bairns level with a close-range shot in 31 minutes after Queens failed to deal with James Craigen’s free kick.
Then he won a penalty in 71 minutes when Lee Robinson brought him down and Aaron Muirhead slammed home the spot-kick.
However, Falkirk were undone in 78 minutes when Dom Thomas was given time and space to measure a cross from the left side and Dobbie got in between Leahy and Grant to place a great header into the left corner.
Falkirk thought they had a winner in 87 minutes but Bob McHugh was flagged offside when he tucked away Austin’s knockdown.
Proud Queens manager Gary Naysmith said: “Last week I publicly criticised the players so for them to put in that type of performance says a lot for them.
“I thought it was a dubious penalty that allowed Falkirk to go ahead and you’re thinking that the lads might not come back but fair play to them for doing so.”