Cardiff chairman Sam Hammam says the actions of Swansea players after their Football League Trophy final win diminish the fans' good behaviour.
A flag from the crowd with offensive words about Cardiff was paraded around the Millennium Stadium by Roberto Martinez, Alan Tate and Lee Trundle.
Trundle also sported a t-shirt with an image insulting to the Bluebirds.
"Thousands of fans came to Cardiff without any trouble, but the players' actions were demeaning," said Hammam.
"There were no incidents from the supporters - years ago there would have been massive fights.
"The players' actions show that they feel they are in a big shadow under Cardiff - they should aspire to more"
"It's a tribute to both sets of fans and to our club who went to a lot of effort to make sure there was no trouble.
"I actually think that the events of the day bode well if Cardiff and Swansea have derby games in the Championship next year. The only problem was with a few players."
Hammam insists that he has always tried to get over the bitter history of rivalry between the two clubs and that he has been delighted to see Swansea's success in recent seasons.
"Since I came to Cardiff I have always tried to preach that the Welsh should stick together and I still maintain that," Hammam told BBC Sport Wales.
"Swansea's strides in recent years have been superb - they've stabilised their finances, built a great stadium and got a hell of a good manager.
"They've won two cup trophies this year and are on the brink of promotion to the Championship.
"They're our Welsh kid brothers and we always want them to succeed.
"But the actions of a few of their players on Sunday just show that they feel they are in a big shadow under Cardiff - they should aspire to more.
"Their actions were worse than those of a fan invading the pitch. It's up to the authorities now, I'm sure they will deal with it appropriately."