Miller owns such brands as Miller, Miller Lite, Miller Genuine Draft and Miller High Life.
According to IRI data for June, analysts said, Miller's US volumes fell by 2.7% in supermarkets and 3.3% in drugstore chains, but rose by 6.6% in convenience stores.
As a result, Miller's market share fell by 40 basis points in supermarkets to 20.5%, while declining by 120 basis points in drugstores to 23.3%.
In convenience stores, the brand's market share remained steady at 18.1%.
By comparison, Anheuser Busch, the US market leader, experienced 2.7% and 4.3% increases in its volumes in drug stores and convenience stores, respectively.
Its supermarket volumes fell by 1%.
Anheuser Busch's market share performance was mixed, with a gain of 40 basis points in drug stores to 44.7%, but losses of 10 basis points in supermarkets to 45% and 130 basis points in convenience stores to 59.4%.
In addition to the fierce competition among brewers in the US market, beer has been gradually losing market share across the wider alcoholic beverages market to wine and spirits in the past few years.
SABMiller CEO Graham Mackay cautioned in the group's 2005 Annual Report, released on Tuesday, that Miller's US growth was likely to be more modest in 2005-06 than originally planned, following higher-than-expected growth in 2004-05.
A more modest performance was also expected across the entire SABMiller group in terms of earnings growth, he noted.
"There is underlying momentum in most of our major markets and we expect further steady organic volume growth, supported by significant ongoing marketplace investment," Mackay wrote.
"Following a number of years of exceptional rates of profit growth, earnings per share for the coming year are expected to continue to grow at a more moderate rate from this higher base," he concluded.