Calls criticising the Scottish Football Association and others making reference to Dunfermline forward Dean Shiels were picked up from a section of the Tulloch Caledonian Stadium during the match which was televised on BBC Alba.
Paul Hartley’s side lost to a Connor Bell second half strike and were knocked out of the Irn Bru Challenge Cup.
A club spokesman said: “Falkirk FC does not condone the singing heard during this evening’s match and apologise for any offence caused.”
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Falkirk fans helped take the attendance into four figures. In total 1078 watched the game at the ground, with more staying at home to watch the TV coverage.
The SFA judicial panel this week banned Bairns striker Kevin O’Hara for eight games after comments made to Pars striker Shiels in the previous round of the competition.