Swindon chairman Lee Power says Bristol City manager Steve Cotterill "showed no class" after
City midfielder Wade Elliott was sent off in the third minute before Michael Smith scored the only goal to end their run of 22 league games without defeat.
"He's done a fantastic job, but showed no class in the tunnel shouting and screaming 'Swindon's done this, and done that'," Power told BBC Wiltshire.
"He should just be gracious in defeat."
He continued: "Great football team he's got there, but they've been battered and that's the end of it."
Town's victory lifted them to second place behind City in the League One table, with just a four-point gap between them.
The game attracted the County Ground's highest crowd of the season of 12,565, almost double the number that watched their in early November.
That poor turnout prompted in January if home attendances did not increase.
"If that's the first time you've come this season, surely you want to come back?" added Power.
"I appreciate not every game's going to be as exciting, but hopefully people can see the signs of what we're trying to do here."
Meanwhile, Bristol City have confirmed they have appealed against Elliott's red card at the County Ground.
The Robins skipper was sent off following a clash off the ball with Swindon's Jack Stephens and, if the appeal is not successful, will face a three-match ban, starting with the visit of Preston to Ashton Gate on Saturday.