The former international striker and Livingston boss, now Martin Rennie’s assistant at the Bairns, was dismissed from the dugout by referee Colin Steven in the League One 2-0 defeat.
The defeat, coupled with Falkirk’s 1-1 draw at home to Peterhead on Tuesday night, leaves the 2015 club fifth in the third tier, three points off the play-offs having played a game more than fourth-placed Queen’s Park.
Now Miller faces a misconduct charge after allegedly breaching rule 203 of the governing body’s guidelines at the weekend. He joined the club alongside his former Vancouver Whitecaps boss in December following the dismissal of Paul Sheerin, but the pair have seen just three wins from 10 matches in charge so far.
He could face a touchline ban if found guilty at the hearing on March 19.