Allardyce's Hammers were denied a penalty early in the second half of their 1-0 third round replay defeat when the ball appeared to make contact with Rafael's arm but Dowd later awarded one to the Red Devils when Ryan Giggs' cross inadvertently struck Jordan Spence's hand.
Whilst West Ham were offered nothing, United went to the spot only to see earlier goalscorer Wayne Rooney sky his 79th effort and Allardyce was furious at the post-match for the inconsistency of refereeing.
"There's no doubt about the difference between Rafael's handball and Jordan Spence's," he told ITV.
"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. The ref did not see Rafael's handball because of his position. But he was in a worse position to see Jordan Spence's than Rafael's."