Swansea boss Kenny Jackett says the controversial celebrations in Cardiff on Sunday were not "pre-meditated".
Lee Trundle and Alan Tate waved a flag with anti-Cardiff remarks after it had been thrown onto the Millennium Stadium pitch by jubilant Swansea fans.
Jackett apologised if any offence was caused and hopes the incident has not soured even further the relationship between the two sets of supporters.
"We don't want to be any more than good sporting rivalry," said Jackett.
"That's the best type anyway when you see good competition and above all good football."
Striker Trundle was also photographed wearing a t-shirt with a cartoon showing a Swansea player urinating on a Cardiff shirt.
"Our season is still to be played out and we have three vital games in seven days"
The Football Association of Wales and South Wales Police are investigating the incident.
Swansea chairman Huw Jenkins said the players were unaware of the derogatory content of the articles which had been given to them by the fans after the Football League Trophy win over Carlisle.
Both clubs have attempted to ease the tensions between the rival fans over past seasons, but Sunday's incident has infuriated Cardiff fans.
And since Swansea could be in the same league as Cardiff for the first time in six years if the win promotion this season, there are fears of violent clashes between the two sets of fans.
Jackett, though, hopes both clubs can put the incident behind them and concentrate on footballing matters.
"The police have asked to speak to us and we'll comply fully with everybody and give them all of the help they need to make any inquiries," Jackett told BBC Wales Sport.
"I can assure everybody there was nothing pre-meditated in the actions and if we've offended anybody the club has apologised.
"It was a tremendous day and a terrific football achievement. The big thing from our point of view is that the major part of the season is still to play.
"We're all talking inside the camp of looking forward now and not looking back.
"There's nothing wrong with those memories, it was a great day. But our season is still to be played out and we have three vital games in seven days."