Gary Holt believes two of the goals his side conceded were “criminal”.
The Bairns lost two goals from set-pieces and another late in the game as they sought another equaliser.
The team was missing Mark Millar and Phil Roberts and had numerous players struggling for fitness. But they were overpowered by the Accies who are joint top of the SPFL Championship - five points ahead of the Bairns.
Mark Beck scored his first goal for the club and levelled the scores before Alex Neil’s side earned the points in the second half.