The Manchester City striker, 29, was found guilty of violent conduct after their 3-1 Premier League win in August.
In its written reasons for the ban, the FA "unanimously felt that the video evidence before them was conclusive".
Aguero, who has scored six goals in four matches this season, is serving a three-match suspension.
"All three Commission members felt that in their opinion, having been knocked off balance by Winston Reid, Mr. Aguero had thrown out his left arm in an aggressive manner that was excessive in force and brutal, which clearly endangered the safety of Mr. Reid," the FA commission's statement said.
"Indeed, even though the point of Mr. Aguero's elbow did not connect with Mr. Reid, his flailing forearm did and this contact between forearm and throat/neck clearly hurt Mr. Reid."
Manchester City contested the violent conduct charge and argued that "the standard punishment would be clearly excessive".
However, the commission noted "the clenched fist of Mr. Aguero as he threw his left elbow towards Mr. Reid, the upward angle of the movement and the force of the movement".
Hammers defender Reid could not talk after the clash, according to his captain Mark Noble, and was substituted.
Aguero served the first game of his ban during last weekend's Manchester derby and will also miss the upcoming home league game against Bournemouth (Sat, 17 Sept) and EFL Cup trip to Swansea City (Wed, 21 Sept).
Sergio Aguero's swinging arm into the throat of West Ham's Winston Reid was "excessive in force and brutal", the Football Association has said.