McArdle will be suspended for the Yorkshire derby at the Coral Windows Stadium - City's third in their last five games - after receiving his second caution of the game in injury time at Oldham's SportsDirect.com Park.
The red card was City's third of the campaign so far following dismissals for Alan Sheehan and Stephen Darby earlier this season.
City cannot appeal against McArdle's red card given the fact that he was dismissed as a result of two cautions but the nature of the defender's sending off does mean he will only be suspended for the Doncaster fixture.
Having previously played every minute of the season so far for City in all competitions up until his dismissal, McArdle will now miss his first game of the 2014/2015 campaign (vs Doncaster Rovers) as a result of his early bath at Oldham.
Speaking about the dismissal, Parkinson expressed his annoyance at the actions of the Northern Ireland international. He said: " We have no complains about the decision (to send McArdle off) - I thought he was stupid.
"Rozzer (Rory McArdle) has been a stalwart player for us for a few seasons now, he is a really honest player who always give his all, but you don't show your care by lunging in on a player with only seconds to go when you are already on a booking.
"You show your care by making sure you do your job and don't get dominated by the player you are playing against."