Swansea manager Paulo Sousa celebrates the 3-2 win over Cardiff
The cost of damage at Swansea's Liberty Stadium, which has been blamed on travelling Cardiff City supporters, has been put at thousands of pounds.
Seats and toilets were vandalised, pipe work ripped from walls and doors broken in the away fans' area on Saturday.
Stadium managers said they were "extremely disappointed" at the damage.
Cardiff City have been asked to comment, and Vince Alm of the Cardiff City Supporters' Club apologised to stadium managers.
Fifteen people were arrested during and after the derby, but police praised the behaviour of the vast majority of the more than 18,000 fans.
In a joint statement Swansea City and Liberty Stadium managers said: "It is totally unacceptable behaviour and we are extremely disappointed".
They said the toilets in the North Stands which housed Cardiff's 1,800 travelling contingent were now unusable, and about 60 seats were also damaged.
The vandalism is being assessed but is expected to cost thousands of pounds to repair.
The managers said: "We will be talking to South Wales Police on what measures are being taken to investigate and what improved procedures we can put in place to prevent this sort of unacceptable damage happening in the future.''
Mr Alm said: "I'm just disappointed that people behave in that way - I don't know what they think they achieve from it."
He said following damage caused in the same fixture last year Cardiff City had paid for repairs.
"If they can't behave I just wish they would not come to football any more," added Mr Alm.
"I just hope that they realise they have probably cost our football club thousands of pounds."
Two people were arrested during the game, which the home team won 3-2.
Another 13 arrests were made outside the ground after the game. The arrests were for public order offences.
South Wales Police said they were investigating criminal damage at the toilets and asked anyone with information to contact them.