Boss Gray talked before the game about losing goals at the wrong moments in games, and his Hibs side once again were undone by conceding at the wrong time.
The visitors had done the hard work to put themselves two up but when MacIver's goal went in, it made for a much more nervy second half.
That stoppage-time goal also means Hibs have now conceded four times in the last 15 minutes of first halves this season - more than any other team in the Premiership.
With Celtic and Hearts now six points clear, Hibs will have to start turning these draws into wins sooner rather than later.
The credit has to go to Falkirk, though, who were clearly galvanised by that goal and presumably whatever John McGlynn had to say at half time.
They kept the pressure on Hibs in the second half and eventually won a corner that led to Henderson's equaliser.
Even after the leveller, Falkirk did not look content to settle for a point, evidenced by the introduction of Brian Graham, Alfredo Agyeman and Scott Arfield with just under 20 minutes left.
They were not afraid to come out and ask questions of Hibs and created more opportunities in front of goal.
Plenty of positive signs for the Premiership newcomers who demonstrated they can go toe to toe with one of the stronger teams in the division.