Sainsbury's announced a 5.3% rise in underlying pre-tax profit to £798 million for the 12 months to March 15, on sales that were up 0.2% on a like-for-like basis.
The group reported that its integration of Edinburgh-based Sainsbury's Bank, previously a joint venture with Lloyds Banking Group, is going "seamlessly".
Sainsbury's profits beat market expectations but worries about a price war led investors to send its shares down 9.5p or 2.9% to 323.9p.
Mr King said: "We think a market with less inflation will be slightly down. But we are going to beat that. We would expect to grow."
The group, which has 82 stores in Scotland, has told the City that this year it expects to match the like-for-like sales growth it achieved in the past year.
Mr King repeated his assertion that despite have headline price cuts by its key rivals Tesco, Asda and Wm Morrison, that there is not a fresh price war in the grocery sector.
"We have always been clear if there are significant moves on price by any competitor at any time, particularly if it is brands, we will cover it off," he said.
He added: "There is always a price war in this market.
"Price is what we compete on. There is a quality war too."
Mike Coupe, who will replace Mr King this summer, said the shake-up in the market could provide an opportunity for Sainsbury to stand out on quality.
"We will always go toe-to-toe on headline pricing but we have a continued opportunity to differentiate our offer compared to our competition," he said.
Figures from Kantar Worldpanel for the 12 weeks to April 27 published yesterday showed grocery market growth at an annual 1.9% - the lowest level for at least 11 years. It said this was due to intensifying price competition. The only large grocer to hold market share in the face of a challenge from the discount grocers was industry number two Asda at 17.2%. Sainsbury's market share slipped 60 basis points to 16.2%
Shore Capital analyst Darren Shipley said: "To date we have believed that Sainsbury has a relatively differentiated offer, which acts as a barrier to the worse excesses of direct price competition. However, at this juncture, we're not so sure, reflecting a recent deterioration in the group's relative performance."
Sainsbury's is pushing on with the roll-out of its convenience store estate, with the recent opening of a Sainsbury's Local store at Edinburgh Causewayside putting it on track to open its 50th Local store north of the Border soon.
On January 31, Sainsbury's competed the £248m purchase of Lloyds's 50% stake in Sainsbury's Bank. It is a third of the way through the integration of the business in what finance director John Rogers said has been a "seamless transition so far".
The core bank and savings business will be integrated in late 2015 with the cards and loans business following by mid-2016.
Mr King said: "Most of out customers do not know we have a bank.
"But when they do find out they say they want to buy a product from us. That is a huge opportunity for us."