All eyes have focused on Europe lately as the financial crisis there threatens economic recoveries in Massachusetts and the nation. But problems in another of state’s key international markets is adding to the worries.

China, which accounted for nearly $1 of every $10 in exports by Massachusetts companies last year, is undergoing a sharp slowdown as global demand for its manufactured products slumps. As a result, Massachusetts-made products shipped to the country — many of which support China’s manufacturing sector — have also fallen sharply.