Graves said a 0.3% slump in pre-tax profits to £9.5m in the year ending April 2009 was caused by a £300,000 hit it incurred on a printing contract for Nisa.
"Our print division lost money on a contract with our friends at Scunthorpe," said the executive chairman, referring to Nisa-Today's.
His comments follow a deterioration in relations between Costcutter, its majority shareholder Bibby Line Group and Nisa. Tension between the parties has been high for months as a result of Bibby's unsuccessful attempts to buy Nisa. Last week, The Grocer revealed that there was a real prospect of Costcutter leaving Nisa after its contract with the buying group expired in 2014.
Graves refused to comment on whether Costcutter would leave Nisa but said he was happy with his company's performance.
Costcutter's turnover increased 5.5% to £567.6m in the year to April 2009, according to accounts filed at Companies House, and has increased by 10% over the past 20 weeks. A new TV advertising campaign was also helping to increase sales, which were regularly breaking weekly records, Graves added.
"We are very pleased with the results and continue to do very well in a tough economic climate," he said. "Retailers see us as someone who offers a good package and we have everything to back it up. If we can keep that up for the rest of the year we will be delighted."
Graves, who is 61, also denied rumours that he is planning to retire soon.
"I will continue running the business for the foreseeable future," he said.
Bibby Line has had two offers turned down by Nisa-Today's board, and last week Bibby Line managing director Sir Michael Bibby wrote to Nisa members directly to raise support for his approach.