The figures for the Walmart-owned supermarket, filed at Companies House, confirm a torrid spell for Asda as it faced stiff competition in the grocery sector.
Like-for-like sales were down 5.7% compared with the previous year.
Pre-tax profits dropped almost 19% to Â£791.7m at the Leeds-based company.
"The grocery market has continued to experience low growth throughout the year and competition in the sector has remained intense. Our sales performance, relative to the market, was behind our expectations," the company said.
Asda, Tesco, Sainsbury's and Morrisons - the so-called big four UK supermarkets - also face competition from German discounters Aldi and Lidl.
Asda suffered more than most and, unlike others, has struggled to fight back. In May, it reported decreasing sales in the first quarter of 2017 - the 11th consecutive quarter of falls - as it continued to lose ground to its rivals.
However, Asda added that despite the disappointing results, there had been an improvement following "strategic changes" under new boss Sean Clarke.
Mr Clarke, who replaced previous chief executive Andy Clarke a year ago, has slashed the prices of everyday items as he attempts to arrest falling sales.
The chain reported a 2.8% fall in like-for-like sales in its first quarter of this year, a moderate improvement on the previous period, which saw sales fall 2.9%.
Analysts have said that a major turnaround is required at Asda.
"Sainsbury's and Tesco have always had more opportunity for differentiation from the discounters, but Asda has chosen to focus on price rather than range and in-store experience, which has clearly been the wrong strategy," said Tom Berry, retail analyst at GlobalData.
"Asda has been flailing without direction for too long, and a comprehensive plan is needed if it is to survive in the highly competitive UK grocery market."
Phil Dorrell, of consultancy Retail Remedy, is a previous marketing chief at Asda. He said that it was a difficult market for Asda and it "had a lot of catching up to do".
"It is not changing significantly or fast enough to pull around the results. It did not get its proposition right," he said.
Sales falls and lower profits at supermarket Asda in 2016 have been revealed in detail in newly-filed accounts.