Sheehan received a straight red deep into stoppage time at the Coral Windows Stadium after appearing to catch Swindon defender Raphael Rossi Branco in the stomach following the award of a free-kick to the visitors.
The dismissal, City's first of the season, means the defender will now miss the Bantams' forthcoming league and cup matches at Milton Keynes Dons, plus the trip to Colchester United next weekend.
The red card topped off a disappointing afternoon for Sheehan after he also saw his third minute penalty saved by Swindon 'keeper Wes Foderingham.
After looking back at replays of the incident, Parkinson in no mood to defend the actions of the Sheehan, who turns 28 on Sunday.
Parkinson said: "We are not happy at all with it.
"When you are having a difficult day, you don't need one of your players losing their discipline.
"We already have Davo (Andrew Davies) out, now we are going to lose Alan for three games. It is costly for us, and he will be fined the maximum he can be.
"We have a small squad and I have said to the lads beforehand that discipline on the pitch is so important.
"The teams who struggle throughout a season normally have the worst disciplinary records as well.
"Ours has been one of the better ones over the years and I am not going to let that change here at the club now".
Parkinson also confirmed post-match that City would need to assess the fitness of attacker Mark Yeates after he appeared to damage his shoulder following a bump from Swindon's Yaser Kasim in the second half.