Sainsbury's posted a 3.8% fall in like-for-like sales growth for its fourth quarter to March 15, bringing a nine-year record of like-for-like sales growth to an end.
It comes after both Asda and Wm Morrison announced plans to spend around £1 billion each on cutting prices.
Mr King said: "What has happened so far is absolutely within the cut and thrust of the market."
He said cuts thus far are "reflective of the normal sums of money that are invested in pricing for one year to the next".
He added: "We are not dismissive of the notion that it may become somewhat more.
"We feel well equipped if that is going to be the environment."
He estimated that half of the investment in price cuts announced by its rivals had gone into cuts in the prices of milk, bread and eggs alone.
Mr King said it had been a "tough market" with low food price inflation . He added that in the comparative period of 2013 Sainsbury had been benefited from the horse meat scandal hitting key rivals.
"The market is growing at the slowest rate since 2005," he said.
But he insisted the company, which is Scotland's fourth largest grocer with 74 stores, is still outperforming its rivals and holding market share at 17%.
Mr King said: "The economy is definitely showing signs of recovery but the outlook for consumers remains challenging. They do not expect their income to rise faster than inflation and they are behaving accordingly."
Sainsbury's said its convenience business grew 15% General merchandise sales also rose.
Clive Black, analyst at Shore Capital, said: "Such a performance will be a particular disappointment to outgoing CEO, Justin King CBE, and perhaps more of a concern and worry to his replacement, Mike Coupe, and the group's shareholders."
After plunging as much as 3.5% in early trading, Sainsbury's shares rebounded to close at 313.9p, up 2.5p or 0.8% on the day. After a recent sell-off in the grocery sector, the stock has fallen to prices last seen in summer 2012.
Sainsbury's completed its buy-out of Lloyds Banking Group's 50% share of Sainsbury's Bank during the quarter. The integration process is expected to take three years.
"We expect the bank to become an increasingly important part of the value that customers receive from Sainsbury's," the group said.
King is to step down in July after 10 years as chief executive to be replaced by commercial director Mike Coupe.