They disappointed again as they failed to break down a well organised Bairns defence. In a bad-tempered clash Falkirk boss John Hughes was sent to the stand after a half-time clash with Michal Pospisil.
Roman Bednar and Kenny Milne were lucky to escape first-half red cards when Bednar caught Milne with a two-footed tackle and Milne got up and pushed the Hearts striker to the ground.
It was Bednar who had Hearts' best chances in the first half. He ran on to Karl Dodd's mistake but was foiled when Scott Higgins saved with his feet. Then the Czech ace screwed a shot wide after Pospisil set him up with a great chance.
Falkirk also had their chances and Pedro Moutinho wasted a clear opening when Liam Craig's cross found him ten yards out, but he could only volley straight at Craig Gordon.
Moutinho tested Gordon again after the interval when he twisted 25 yards from goal and fired in a right- foot effort that Gordon smothered.
Hearts also went close from distance when Neil McCann's 30-yarder was plucked out of the air by Higgins.
Hearts pushed hard for a late winner and Pospisil should have netted from Saulius Mikoliunas' cross. Bednar created another chance and blasted a late volley over the bar but for the second time in a week Hearts couldn't win at home.