"Unite have failed to ground British Airways and we are continuing to fly and we are continuing to work," Walsh told reporters at the International Air Transport Association in Berlin, The Guardian reported.
On Sunday, the airline flew 72,000 passengers, he said.
Walsh said he had pledged not to discuss details of the negotiations. He said the airline would "continue to make progress on our cost base."
He said there was "no trade-off in this" but the airline had options for cutting costs.
"We can do that in many different ways," he said.
Walsh was criticized for leaving Britain during the strike, but Unite General Secretary Tony Woodley was also criticized for taking a vacation in Cyprus just before the latest five-day walkout began, the newspaper said.