Mr Walker confirmed yesterday he was appealing a High Court decision last month that dismissed his opposition to the council contributing $37.5 million towards construction of the $198 million stadium.
Mr Cairns said he was "flabbergasted" when told of the appeal last night.
"He was resoundingly, robustly defeated and, quite frankly, I'm flabbergasted that he would do this.
"The court awarded costs. Today, it remains unpaid.
"If, indeed, he is able to get a fixture - and that would be an 'if' - from our perspective we would look for total satisfaction on costs."
Mr Walker said he had paid as much as he was allowed to pay as an undischarged bankrupt and the council had sent the money back.
Mr Cairns said the amount sent was $100 and Mr Walker was "playing games".
Mr Walker said he had sent his appeal documents to the court, as they had to be filed by tomorrow.
He first took court action in May, when he attempted to gain an interim injunction against the council.
At a June 4 hearing, Justice Graham Lang questioned many of his arguments and, a week later, released a decision dismissing the case and awarding costs to the council.
Mr Walker said he did not want to go into the details of his appeal until the documents had been lodged, but said he would release them after that date.
He said there was "an awful lot missed out" of Justice Lang's decision.
A High Court spokeswoman said yesterday afternoon the appeal documents had not yet been received.
