The Hang Seng index ended down 0.1pc at 26,435.67 on Friday, while the China Enterprises Index also lost 0.1pc to 10,375.65.
HSI shed 3.4pc for the week, while HSCE lost 2.9pc.
Hong Kong's central bank lowered interest rates on Thursday in step with a rate cut by the US Federal Reserve, just as months of anti-government protests and fallout from US-China trade tensions start to take a toll on the economy.
The rate cut comes after more than 100 days of anti-government protests in the city, with violence escalating over the summer.
Last weekend, police fired water cannon and volleys of tear gas to disperse protesters, many of them masked and wearing black, who threw petrol bombs and set fires in Causeway Bay and the nearby Central district.
In a direct challenge to Beijing, some protesters threw bricks at police outside the Chinese People's Liberation Army base and set fire to a red banner proclaiming the 70th anniversary of the founding of the People's Republic of China.
Beijing on Friday cut its new one-year benchmark lending rate for the second month in a row, a step by the central bank to wrestle down borrowing costs and support the economy as the Sino-US trade war drags.
However, cautious easing seemed to offer little support for mainland companies listed in Hong Kong on Friday.
Around the region, MSCI's Asia ex-Japan stock index was firmer by 0.57pc, while Japan's Nikkei index closed up 0.16pc.
The yuan was quoted at 7.09 per US dollar at 0814 GMT, 0.1pc firmer than the previous close of 7.097.
The top gainers among H-shares were China Communications Construction Co Ltd, which ended up 6.35pc, followed by China Railway Group Ltd, gaining 3.97pc and CRRC Corp Ltd, up by 3.01pc.
The three biggest H-shares percentage decliners were Shenzhou International Group Holdings Ltd, which ended down 2.96pc, Guangdong Investment Ltd, which closed 2.11pc lower and China Pacific Insurance Group Co Ltd, down by 1.91pc.
At close, China's A-shares were trading at a premium of 29.93pc over Hong Kong-listed H-shares.