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.”