Blues were leading 2-1 in injury time at Huish Park when Yeovil's Byron Webster lobbed the ball into an empty net after Birmingham goalkeeper Colin Doyle had kicked it out of play following an injury to Blues defender Dan Burn - with City manager Lee Clark furious the ball had not been given back.
Glovers boss Gary Johnson admitted he told his team to play on having grown frustrated this season by potential time-wasting tactics, although he apologised to Birmingham after admitting Yeovil's "ungentlemanly" behaviour.
Blues eventually held their nerve to win 3-2 in a penalty shoot-out after the match finished 3-3 following extra time, but Clark still vowed to lodge his complaints about the controversial incident.
And it is understood a letter has been sent to the FA's regulatory board although in the firm knowledge that no rules have been breached, with Clark keen to now draw a line under the matter.
Speaking immediately after Tuesday night's match, Clark said: "I might be wrong but my parents made me grow up to be a good sportsman - win, lose or draw.
"I'm going to go down the right channels to complain. I think something has got to be done."
With the scores level at 2-2 after 90 minutes, Yeovil moved ahead in extra time through Luke Ayling but then immediately allowed the visitors to walk in an unchallenged equaliser from Lee Novak as compensation.
Tom Adeyemi's penalty in the shoot-out took the 2011 League Cup winners into the third-round draw.
Speaking after the match, Johnson called upon referees to look at incidents in which teams kick the ball out late on in matches for their own player to receive treatment.