This is Protestant/New Atheist bad history. Innovation didn't stop in Europe for several centuries, only to be sparked by contact with Islam.
However, it is true that in the Western Roman Empire, lack of support for education and similar projects made the literacy rate fall and reduced the numbers of available writings from the period (hence, a dark age because we don't much written about it). It's also true that in the Eastern Empire, ancient Greek works (by polytheists) were preserved by the Orthodox Christians, who shared them with Muslims, who shared them with the western Christians, and these writings were the subject of study and debate for a couple of hundred years before the Renaissance.
If you are really interested in sorting the good history from the bad, an atheist named Tim O'Neill
runs a website devoted to correcting the bad history promulgated by other atheists.