An independent FA regulatory commission said in partly redacted written reasons that it considered the midfielder's actions to have been "highly violating and intentional foul play".
"The commission did not accept the player's view that neither of the acts were intentional," it added.
"The Commission recognised that there was no plausible explanation to be touching an opponent's private body parts during a game (especially when the match itself was not in motion)."
The incidents happened during the League Two (fourth-tier) side's League Cup 2-1 first-round loss at Cardiff City last August.
Clarke, 33, was also fined 2,750 pounds ($3,701) when he was banned last month after maintaining his innocence.
Swindon condemned the ban at the time, saying in a statement that it believed "the decision falls short of the standard of proof beyond reasonable doubt and was instead based on the balance of probabilities.
"As a club captain, Ollie's character and integrity have never been in question, and he continues to have the full support of the club, the management, and his teammates."