The Hammers boss was furious with Dowd's performance in the FA Cup defeat at Manchester United, and he accused the official of bias towards the home team.
Dowd pointed to the spot after Jordan Spence was adjudged to have handled a Ryan Giggs cross, but his refusal to award West Ham a penalty when Rafael deflected the ball on to his own arm left Allardyce fuming.
"There's no doubt about the difference between Rafael's handball and Jordan Spence's," he said afterwards. "Spence plays for West Ham and the away team, while Rafael plays for the home side at Old Trafford.
"With Rafael, the ball hits his hand, but no penalty is given. With Jordan Spence, the ball hits his hand and it's a penalty. You see it time and time again at Old Trafford."
Allardyce's outburst has incurred the wrath of the FA disciplinary committee, who issued a statement confirming the Hammers manager had been charged.
The statement read: "The charge is in relation to an alleged breach of FA Rule E3 concerning media comments which questioned the integrity of the match referee and/or match officials in general and/or implied that the match referee and/or match officials in general are motivated by bias and/or brought the game into disrepute."
Allardyce has until Wednesday 23 January to respond to the charge.