The former Tottenham and Aston Villa boss repeatedly swore at referee Mark Brown at half-time during a 1-0 defeat at Bury on 11 February.
Sherwood, 48, has already served the ban, while he was also fined £2,000.
On Monday, the FA published the written reasons for Sherwood's suspension.
It includes a report from Brown, which describes Sherwood "pointing aggressively in my face", as well as claiming that the former England midfielder used an expletive on five occasions.
Sherwood was appointed Swindon's director of football in November 2016.
They are 22nd in League One, seven points from safety with seven games remaining.
Swindon Town director of football Tim Sherwood was given a two-match stadium ban because of a foul-mouthed rant at a referee, the Football Association says.