Great question. While the American Revolution is a critical moment in American history, in the context of global politics at the close of the 18th century, it was not a major event. The Ottomans didn't register it as such, at least.

In 1776, the Turks were still embroiled in their war with the hated Persian enemy and didn't have a reaction to the revolution worth mentioning. However, it did have unexpected consequences for them in the form of the Greek war for independence in 1821. The Greeks were directly inspired and influenced by the American Revolution, a point that the Ottomans recognized only too late.